It looks like the shop put in an AH battery (YTX5L-BS... KYMCO KY D410) and that's what's called for in the manual (12V4AH). What's the difference between A and AH? Plus, it looks like the shop only thinks it put in a 5 amp battery. The web seems to indicate that YTX5L-BS is 4AH.
A is Amper, electrical current.
Ah is Amper-hour.
4 Ah means that accu should provide 4 A of electric current for 1 hour or, alternatively, 1 A for 4 hours.
I think that there is no big difference between 4 and 5 Ah and they can both be used.
Of course, you could not charge 40 Ah battery in a circuit dimensioned for 4 Ah.