Let $Z\to X$ be a closed immersion of schemes. Assume $\mathcal{O}_Z$ and $\mathcal{O}_X$ both are coherent sheaves of $\mathcal{O}_Z$, resp. $\mathcal{O}_X$-modules.

In particular, the coherent sheaves on $Z$, resp. $X$, are precisely the finitely presented $\mathcal{O}_Z$, resp. $\mathcal{O}_X$-modules.

It is true that if $\mathcal{F}$ is a quasi-coherent $\mathcal{O}_Z$-module of finite type, then $i_*\mathcal{F}$ is a quasi-coherent $\mathcal{O}_X$-module of finite type (in general. No need of coherence of the structure sheaves).

Is it true, under the assumptions explained up above, that if $\mathcal{F}$ is afinitely presentedquasi-coherent $\mathcal{O}_Z$-module, then $i_*\mathcal{F}$ is also finitely presented?