Mentioning that a part of the thesis was done at another university in my PhD thesis
A simple statement such as "This study was carried out at X University under the supervision of Professor A" would probably suffice, but check with your supervisor in case there are any local regulations that you have to follow. 

For example, my university requires every PhD thesis to have a "declaration" statement after the abstract, in which you list things like funding sources, collaborators and any publications resulting from your research. Your university may require something similar, in which case you would put this statement there.