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Gentlemen - I got my new bystarter and installed it this weekend.
After installing, I started the bike up and it started great.  I went for a good 10 minute ride and as soon as the bike warmed up and I came to a stop the bike died.  I was able to get the scooter started again and off on my way I went again, but again when I come to a stop or even come close to idle the bike stalls again. In fact, at low rpm(3K) the bike will began to misfire when I am coming to a slow, but take off again before letting the bike make a complete stop.  The bike seems to have great top end power and pulls without issue. 
I brought the bike back into the garage and removed the new bystarter and reinstalled the old one and the bike performs the same.
Then I decided to remove the needle from the bystarter and install without needle.  The bike seems to run better this way but not perfect. This almost points to needing more fuel, so I rechecked my slow speed jet and it is clean and clear.
I am going to just order another carb from Amazon and continue testing.  I might have to order a jet kit and intake boot rubber modifier to install like Ruffus did on this scoot.
I'll keep everyone updated.

thank you,
Rey

Hello Gentlemen and thank you for all the responses. 
I think I may have found out something and this might help you out as well Iahawk, as I think the bystarter is the source of my issue.  Here is what I did.

Yesterday afternoon I started the bike and let it run and idle which it does fine when cold.
When it warmed up and started to misfire and die at idle, I reved it to 5-6K rpm and verified that the bike runs fine at high rpm.  I did several times and the bike begin to run worse and worse especially at low rpm (under 3k).  I purposely wanted it to be acting up so I can check the bystarter circuit.  Everything checked out with the bystarter circuit, even the needle had extended out about  4-5mm.  Still not trusting the bystarter operation, I removed the bystarter completely off the carb and used my thumb to cover the open of where the bystarter mounted. What do we have here..........I restarted the scooter and .................. it started to idle at 1800. WHAT......?
With my thumb covering the bystarter opening (bystarter sitting on the ground) the bike runs perfect.  Idle at 1800, revs to 9k all on the stand, I can turn off the scooter and restarted like it was running on fuel injection.
So for now, I have ordered a new bystarter that I will install, maybe mine is leak and not sealing completely (not sure).  The unit will be here tomorrow for about $25.00 USD from Amazon.  I will report back when I install the new one.  The o-ring on my old bystarter is intact, but it does look like it has shrunk over the years.  When I sprayed carb cleaner over this area I did not get a change in rpm.  Maybe the needle is not sealing completely?

CROSSBOLT - I have over 12v when cracking, so I think that is good.

Ruffus - my Carb has the mix screw positioned differently than the pic you provided.  Mine can be adjust from the top, while your picture shows one adjust from the side.  My mixture screw is a D shaped and was capped.  I'll try to see if I can somehow get a picture up.

Thank you all.  I think we are all learning something new everyday.

In terms of the mixture screw, I do not have the correct D shaped driver for this in my kit of 10 special drivers for carburetors. The D shaped one I have is either to big or too small, but I will see what I can create.  If anyone has the information on the correct driver "D" for this carb?

Thank you Ruffus for the information.  Let me update you and see what you think. I really don't think the mixture screw is an issue at the moment.

I had a rough time this morning getting the scooter to start after the carb install.  Here is what I did.
I installed the carb and did a TPS sync with the information provided by Iahawk.  Turn the throttle all the way to WOT and then turn on ignition, wait 8-10 seconds and slowly close the throttle. then turn off ignition.
The scooter was a cranked and no start.  I took off air filter and sprayed some carb clean into the air tube behind carb. More cranking and no start.  I figured I better check for spark, so I took out the plug.  BTW - Air filter looks brand new and plug looks real good as well(new).
I found the plug was wet(fuel), so I cleaned it up and cranked the motor with the plug out to dry the cylinder.
We have spark, so I reinstalled the plug and tried again.
Crank, crank, crank oh no battery is not getting low.  Throw the charger on the battery, Battery is brand new and holds 12.6v, but I have been cranking a lot.
Finally the motor starts for a split seconds and dies.  A few more cranks and same, starts for a split sec and dies.  I tried to give it gas and nothing.  More cranking and finally the bike starts and I give it gas and she comes to life.  BTW – this happened about 10-15 times before she finally started.  Moving the throttle back and forward trying to keep bike alive as she misfires.  Finally she smooths out and sounds good.  Idles perfect and sounds strong when I give it gas.  I turn up the idle on the center stand and let the rear tire spin while holding 4-5k rpm. I leave the bike running for 15 mins.  I turn the idle back down to 1800-2k and everything is perfect for a minute or so at the most. 
Then the engine start to misfire again and then dies.  She starts right back up but now when at idle, the engine starts to misfire and die.  Starts back up, idles fine for a few seconds and then the engine starts to misfire again and die. Oh no, what’s going on here?  Now engine begins to act up even more and cranks but doesn’t start until I let go of the starter button.  Again she idles, but begins to misfire after a few seconds and dies unless I hold the throttle open to over 3k.  She is acting the exact same way before I removed the carburetor for a cleaning and drained the gas.  Please keep in mind that I didn’t find the carb to be dirty or plugged in anyway when I took it apart.
I purchased this bike recently with a dead battery and not running even though she started right back up after just a new battery.
During the time the scooter was running on the stand and the idle was good, I sprayed carb cleaner all around to see if I had a vacuum leak and I did not find any leak.
I have moved the spark plug cable around and nothing changes.
I moved the TPS wires and tugged on the sensor and I did notice some changes, but not significant.

What does the TPS information do in this case?
This bike is not fuel injected, is there an ECU?  I understand what a TPS does, as I work on all my cars.
What can be causing the misfire? lean misfire?

Why am I getting a misfire at idle, but not at high rpm?  I do not think it’s the idle jet honestly because it will idle on its own sometimes.

Maybe it has something to do with temperature as it seems that the idle issue gets worse as it warms up.
I am beginning to think that maybe this is why they stop riding it.
I have rebuilt numerous automotive carburetors over the years, Holley’s, Edelbrocks etc. I have taken and rebuilt a dozen scooter and motorcycle carburetors over the years.  I have never had any issues, even old tractors and an old model A Ford I had with an updraft carb.

So my problem now is a misfire at idle and hard to start. She seems to have lots of power if I hold the gas open and put a load on with the rear brake on the stand. Is this a lean misfire?  The bike seems like it could run all day at 6k rpm.

Sorry for the long write up and thank you for all your help in advance.
Which after market carb did you buy?  I am in the USA, by the way.

Thank you! I guess better pop the cover off and take a peek.

Hi Everyone!
I just got a Movie 150 that had been sitting for over a year.  I plugged in a new battery and the little scooter started right up and idled like a champ, but after some driving around (maybe 10 miles) the scooter now dies when coming to a stop and will sometimes restart, but it does not want to idle when I come to a stop.  When it does restart it will idle, but it dies when I give it some gas. I find it odd that it does want to idle when it finally starts, but dies when I give it gas to take off. It also sometimes just cranks and cranks, but no start. It has about 3600 miles and for the most part seems to have been taken care of.  Oil is clean, air filter looks new and the plug also looks great.
I have now drained the fuel and topped off with fresh fuel.  I took the carburetor apart to check the jets and float level, all checked good.  Jets were very clean, but I went ahead and dipped the carb for 4 hours in a bath of Berryman Chem-dip twice.  Fuel filter is not plugged and the float bowl has fuel when I have drained it a few times thinking I had bad gas.  I also checked the fuel pump by applying vacuum and it is working.
I am thinking that maybe the TPS needs to be adjusted or synced. My questions are,

1. Where is the mix screw and
2. How do I sync the throttle position sensor?

I appreciate anyone's advise on this nice little bike and what I should do as maintenance at this point.  It's 8 years old and has 3600 miles.

Thank you,
Rey