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If you are on SSDI, social security will not care how you spend the money and what you do with the money you get from selling your home.
They will not mind if you give money to your mom.
The only social security benefit that would be impacted by this would be SSI, which is a low income benefit.
But, the sale of your home will not impact your social security benefits at all.
There is no time limit for spending the funds from the sale.
You will owe no capital gains tax if it was your primary residence and your gain is less than $250,000