This process is called a probate.
A probate is a legal process in which a will is reviewed to determine whether it is valid and authentic. This terms refers also to the general administration of the deceased person's will, estate and possessions.
During a probate, the court appoints an executor named in the will or an administrator if there is no will. This person collects and evaluates the assets of the dead person, pays any liabilities remaining and distributes the assets of the estate to the beneficiaries named in the will or established by the executor.