I think it is the same AN McMahon who resigned in early Jan 1921, who rejoins in late Jan 1921.
1897 Born Los Angeles, USA
1901 census at 23 Trevor Street, Holywood, Down)
1911 census at 16 University Street, Belfast
1914 Sep 14. Enlists in R Irish Rifles but is soon dismissed because he misstated his age. The address he gives on this enlistment is same as on MIC in Belfast. Mother Lydia. He says he was born Los Angeles, USA, and that he was an apprentice in Linen Business
1914 Nov 19. Dismissed because of age mis-statement. It says he was 17 8/12 when dismissed
1915 May Landed in France.
1917 Apr 26 Commissioned 2nd Lt in Connaught Rangers
1917 Oct 26 Transferred to R Irish Regt..— A. N. McMahon (from Conn. Rang.). with seniority from 26 Apr. 1917.
1918 Oct 26. R Irish Reg. Temp. 2nd Lt. A. N. McMahon to be temp. Lt.
1920 Dec 30. Joined ADRIC with service no. 1426. Posted to N Coy
1921 Jan 16 . Permitted to resign. I have assumed it is the same man re-joining a few weeks later. There are no other likely officers in the records as "A N McMahon"
1921 Jan 31. Re-joins with service no 1618 . Posted to M Coy
1921 Feb 19. Posted to I Coy
1921 May 26 Posted to Z Coy
1922 Jan 16. Posted to Depot Coy and discharged on demobilisation of ADRIC
1922 Feb 15 Gazetted out. R. Ir. Regt.. Temp. Lt., and: retain the rank of Lt.: — A. N. McMahon