Praise be to Allah.
Yes, you must certainly fulfil your promise and give that money to the mosque that your mother wanted to give it to, as that you promised to do. It is part of honouring her and treating her kindly to fulfil this promise, in the hope that Allaah, may He be glorified and exalted, will accept its and benefit her thereby. This is part of honouring her and treating her kindly. If the mosque that your mother wanted to support has no need of it and its expenses are covered, then you may give it to any other mosque, but as we have mentioned, you should not neglect this promise and fail to give this money, rather you should and most certainly must fulfil this promise, as a way of honouring your mother. And Allaah knows best. End quote.