Moving in with a partner

Hi I am new to the group.but pleased I have joined when I have been reading through.came highly recommend to me.
I need a bit of advice please.i am on esa income related.in support group.and pip enhanced rates. No sdp.and am looking to move in with my partner.she is esa income relared sdp and pip both enhanced..would this be a change of address because she can't move to universal credit with legacy benefits,and she doesn't want to move to universal credit.because she isn't well enough at the minute to go through all forms and things,because she has always been long time sick..or would it be a full universal credit for both of us and have to go through everything again.

Sorry it's so long asking you questions, your help would be much appreciated
Thankyou

She has sdp but I don't because I live with parents.but both have esa income related.mine is 12.50 or something a week.and both enhanced pip.and partner has both enhanced pip too.so would it be me just informing them I am moving in and her informing them or a trigger for universal credit.

Thanks

She has sdp because lives on her own at minute.and both enhanced pip mobility and care component.but I don't claim sdp because I live with parents.i know at minute her benefits are protected from change to universal credit.so would I just have to contact them and say I am moving and her contact them to say I would be moving in.or would it trigger a full universal credit for both.
Thankyou

Thank you..i am just struggling to understand it all at minute because previously always worked .we have both paid contributions from working,so one of us wouldn't be able to claim our state pension ? Also if I inform them would she have to claim for me on her esa with me closing mine.so sorry for keep asking.
Thankyou