Is it possible to remove the battery from MacBook Pro (A1502) and use in a different MacBook Pro? My MacBook Pro battery is faulty, it never charges past 2%. As I'm unable to work I've purchased a new battery but it will take 4-5 days to arrive

Could I remove the battery from my MacBook Pro (A1502) and run it in my other MacBook Pro? This would enable me to work.
Typically, no.  Batteries are not interchangeable.

The exception being that they have both the same model (i.e A1502) and the same EMC number (found on the bottom lid).

Model numbers can be reused from one generation to the next, however EMC numbers are unique manufacturing codes.  If those numbers don’t match, your batteries likely won’t match up