Assume we have an affine scheme $A$ that comes with a closed immersion into a smooth scheme $i \colon A \hookrightarrow M$, which is not necessarily affine.

Does there exist an affine open subscheme $j \colon V \hookrightarrow M$ such that $A$ already embeds in $V$?

Expressed in Diagrams, does there exist an affine open subscheme $V$ of $M$ such that we have a factorization

i A (----> M \ / \ / V ?