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Your son would have to pay tax on the gain. He starts with the original cost that the mother had and then he adds his costs to repair the property. That is his basis and a loan would not change that.
Getting a mortgage does not reduce his capital gain. As he is being given the property his cost to start is the same as the mother's cost. The additional costs for capital improvements does add to the cost for him.
If he keeps the property for longer than 1 year he can use the lower Capital Gain rates. If sold before that he pays regular rate.
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