It would be useful that you mention the battery numbers that are printed upon them.
I can confirm that the A1322 battery from a MacBook Pro 13'' loads correctly when attached to the MacBook Pro 15'' A1286 8,2 Early 2011.
Both batteries operate at same voltage. The one from the 13'' has smaller capacity.
The connector of the A1322 batttery is at a different location than thus of A1321 / A1382 batteries, so that you cannot insert the battery into the MacBook 15'', at least without replacing the 2.5'' drive by a shorter SSD modul.
However, you can hold the battery with your hand. For me, this proved useful to check that a newer battery would fix a jerky mouse cursor issue.