All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
The opinion that is deemed preponderant by the scholars regarding a dead person upon whom Hajj had been obligatory with certainty but who did not perform it during his life is that Hajj should be performed on his behalf from his estate.
Accordingly, Hajj should be performed on behalf of your wife's mother, and it is not necessary to transfer the amount to a certain address. Rather, what is required is that Hajj be performed on her behalf by whatever means possible. If a person volunteers and performs this obligation on her behalf, this is sufficient. But, if there is nobody who does so, then a person should be hired to do it.
There are other things that can be done and benefit the deceased. However, they are only recommended acts that cannot reach the rank of the obligatory Hajj. So if you can do both matters, i.e. to perform Hajj on her behalf and dedicate the rewards of other good deeds, like that which we have highlighted, to her, then this is better. But if you cannot combine the two, then it is more appropriate to perform Hajj on her behalf, since a recommended act cannot be compared to an obligation.
Allaah Knows best.