He was not in the Reserve until 1924 unless it states something like 'Class Z' on his medal card. A certain number of men were discharged to Class Z Reserve in 1919 in case fighting started again. The Class Z Reserve was disbanded in 1920 after the major peace conferences.
You may be lucky as they may have obtained a copy of his WW1 record and added it to his 1924 enlistment papers. If so his record would not have been stored in the Arnside warehouse that suffered the fire in 1940.
I would think the chances are good as normally a recruits states on his second set of attestation papers only brief details such as 'ASC four years time expired'. For the Records people to have the actual enlistment/discharge dates may suggest there is more information in the file. You need to ask for a copy of the whole file, and not just a summary.
Ken