If in the course of proceedings to obtain a grant of probate or of letters of administration under section 16, section 18 or section 19 of this Act any person appears and establishes his claim

(a) to probate of the will of the deceased; or

(b) to letters of administration as next-of-kin of the deceased, and gives such security as may be required of him by law, the court may grant probate of the will or letters of administration accordingly, and shall award the Administrator-General the costs of any proceedings taken by him, under those sections, to be paid out of the estate as part of the testamentary or intestate expenses thereof.