Python: Check if values match (2 different sources) and if so return 2 columns from one source to the other

Question

I have data in 2 different spreadsheets (see below example).

I am trying to work out how to do the following:

If A matches B, then copy B and C into A. I would like B and C to be at the very end of all the other columns in A if possible.

I have been playing around with groupby but haven't been able to make anything stick.

Any help would be greatly appreciated :)