12-week linking rule, moving to new-style ESA

Getting tied up with this one ..

Client receiving old-style (C)ESA, support group. We become a UC full service area. Starts 16+ hours work, which lasts less than 12 weeks. Goes to reclaim ESA, is told can’t claim, so has to claim UC instead and serve a new assessment phase for WCA.

How should the 12-week linking rule apply here? It exists in both sets of regs, does it make a difference that the new claim would be for new-style ESA? Shouldn’t he go straight into the Support Group? Does he have to meet the contribution conditions again at the time of the new claim for an award of new-style ESA?

edit: for ref https://www.rightsnet.org.uk/forums/viewthread/12954/#60307