Ok, I’m reading the paper Homology and cohomology of associative algebras. A concise introduction to cyclic homology by Christian Kassel, and on page 19 he says that Hochschild homology is Morita-invariant, by which he means that if $R$ and $S$ are two Morita equivalent rings then $$ H_*(R,M) \cong H_*(S, Q \otimes_R M \otimes_R P) $$ (here $H_*$ denotes Hochshild homology). He then shows how $$ H_*(M,M) \cong H_*(S,S) \,, $$ and states that
Hochschild cohomology groups are Morita-invariant in a similar way.
I wanted to find a proof or reference for this? Just wanted to be completely sure about this and avoid any confusion, in what similar way are Hochschild cohomology groups Morita-invariant? Please be nice lol.