I believe that Finnair charges GBP 18 for transferring Avios from one account to another.
If you move your wife's Avios from BAEC to Finnair and then pays the transfer fee to transfer her Avios to your Finnair account, I would assume that you can transfer back the Avios from your Finnair account to BAEC and then onwards to your Privilege Club account?
No idea if this works, just thinking out loud.