Advice re mandatory reconsideration

My partner is claiming universal credit (since January) and has been handing in sick notes. He received a letter last week telling him he’s been put in the wrag group but he will be appealing this as he feels he meets the criteria for support group, the support group. He has asked for the report and once he sees where they failed him he will apply for a MR...... however, we are planning to move in together in the next few weeks so when he does the MR he won’t be on universal credit anymore he’ll be on my income support claim. Will he still be able to ask for a reconsideration for the time he was on universal credit (so that if it’s over turned he’ll be entitled to back pay from when he started the claim in January)?