Let $R$ be an integral domain, $S$ be a finitely presented $R$ algebra. Then for a flat $R$ module $M$ which is also a finitely generated $S$ module I need to show that $M \otimes_{R}T$ is a fintely presented $S\otimes_{R}T$ module where $T$ is the quotient field of $R$.

My attempt : Since $M$ is finitely generated $S$ module then we have an $S$ module surjection $$S^{n_1} \rightarrow M.$$ Since tensor product is right exact we would have a surjection $$S^{n_1}\otimes_{R}T \rightarrow M \otimes_{R}T$$, now if I can show that the kernel of this map is finitely generated I will be done and here is what I feel like finitely presented $R$ algebra property of $S$ might be used , but I am unable to progress further from here.

Any hint or suggestion is much appreciated, thank you.