No. Your son cannot claim any of the expenses associated with the mobile home since he does not have any ownership in the mobile home.
Generally, if he would own the property and put the money into it, this would be added to the cost basis of the property and then depreciated if it is a rental property. If it does not become a rental property, then the remodel is added to the cost basis. Since he does not have ownership in the property, this would not apply to him.
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