What if your father has died left 2 life insurance policies one to you one to his mother-who pays for the funeral and who inherites his personal property and is responsible for his debts?

The beneficiary on the policy to you (assuming you don't have any financial obligations directly related to your father's death) is free and clear. Unfortunately for the mother, she's now responsible for the debt of the funeral, but depending on the value of your father's estate, the estate could be sold and help offset the cost of the funeral expenses.

Otherwise, both policies are capital gain income, and post taxes they are the property of the beneficiaries.