(a) If satisfied, upon the hearing, or upon the report of a master, that the death of the presumed decedent has been established, the Court of Chancery shall so decree, and the Court shall determine in such decree the date of such death.
(b) The Register of Wills shall issue letters of administration to the person thereto entitled, or receive for probate the last will and testament of such presumed decedent, and, if duly proved, admit the same to probate and issue letters testamentary thereunder. The letters, until revoked, and all acts done in pursuance thereof and in reliance thereon shall be as valid as if the presumed decedent were actually dead.