Will the SIM card from an Express Prime 3 work in a Galaxy A01?

Yes, Both Express Prime 3 and Galaxy A01 use a Nano-SIM!

As per the Galaxy A01 User Manual, Your Galaxy A01 uses a nano-SIM card. A SIM card may be preinstalled, or you may be able to use your previous SIM card.

 

How to Set up SIM card lock on Galaxy A01? please refer to AT&T PREPAID Samsung Galaxy A01 user manual, which is available for download here.