I'm going to complicate this a bit.
My research shows John Price Jones 638/53857 was from Cyttir, Llangoed, Anglesey. He served overseas with the 1st Battalion from early September 1916. Possibly had a brother William Jones was in the Labour Corps Pte 257742(no overseas service)
Many 2nd line Territorial Force men were sent over after the Somme had started in earnest and, because they were then posted to 'Regular' Battalions, they were given a 'Regular' number. RWF 5xxxx series are littered with them.
Re the 638 number. It would make sense, given the Anglesey connection, for this to be a 6th Battalion number (Carnarvon & Anglesey) but this number was allocated to Richard Richards of Tremadoc (in June 1909. Service papers extant)
638 in 5th Bn (Flintshire) would have enlisted around April 1909.
6638 RWF was also a John P Jones. I have no further details yet on him other than he didn't go overseas till after 1/1/1916. This number in the Regulars would have enlisted 1901. In 4th Battalion would have enlisted 1910 and in Special Reserve (most likely) in June/July 1915. It would be far too high a number for the other 3 TF unots (5th, 6th and 7th) in March 1915 which is when the will was signed.
Can you link your man to Anglesey?
What wartime address have you got for him?
Gwil