taking out a Jasmine plant

I have a 4 year old Jasmine plant that was growing on my pergola/decking that I have thinned back but now I find I need to move it entirely as it is in the line of build of the conservatory I am having instead of the decking.  Am I best to cut it right back to the base and dig out the root to re-plant?  Try to dig out the root with 'runners' still on it - it is quite big.  Or should I just give up and buy a new one I have to have a Jasmine plant because my granddaughter is called Jasmine and it was planted for her and with her when she was 4 years old.