Invariance of generalised Reynolds ideals under derived equivalences

For any algebraically closed field $k$ of positive characteristic $p$ and any non negative integer $n$ K"ulshammer defined ideals $T\mathrm{\_}n{A}^{\perp }$ of the centre of a symmetric $k$-algebra $A$. We show that for derived equivalent algebras $A$ and $B$ there is an isomorphism of the centres of $A$ and $B$ mapping $T\mathrm{\_}n{A}^{\perp }$ to $T\mathrm{\_}n{B}^{\perp }$ for all $n$. Recently H'ethelyi, Horv'ath, K"ulshammer and Murray showed that this holds for Morita equivalent algebras.