I've trawled through some service records. Unfortunately none seem to survive in the range 32580-32599 but I found three in the block 32570-32579. Of these, that for John William Blanchard is the fullest. He transferred (from RA via Tank Corps) to 4th (Reserve) Battalion East Lancashires in August 1917 and was given the new regimental number 39123. He was posted to the BEF (1/4th East Lancs) 12/13 December 1917. Whilst at Base Depot, Etaples on 16 December he was transferred to South Lancashires, and posted to 1st/5th battalion and given the new regimental number 32573. On 20 December 1917 he joined 55th RD? [presumably a divisional reinforcement depot or similar] , joining the battalion in the field on 6 January 1918.
The other two records I found agree with this one insofar as they have the man being posted to an Infantry Base Depot in France on 12/13 December 1917 and then a transfer to the South Lancashires and posting to the 1st/5th taking place on 16 December 1917. This is inevitably a bit conjectural, as I said before, but I think the pattern of 12/13 December or thereabouts to France, rebadging at base depot a few days after, and joining the battalion in the field earlyish in January 1918 is about as close to the truth as we are likely to get.