End extension models of $I\Delta_0$

Question

Recently I'm thinking about below question, but I can not prove or disprove it.

Is it true that for every model $M\models I\Delta_0$ there exists a model $M'\models PA$ such that $M'$ is end extension of $M$?

How can this statement prove or disprove?

Thanks.

Answer 1

I asked this question in math overflow and thanks to Joel David Hamkins now I know the answer.

By Incompleteness theorem $I\Delta_0 \nvdash Con(I\Delta_0)$, so there exists model like $M\models I\Delta_0+\neg Con(I\Delta_0)$. On the other hand $PA\vdash Con(I\Delta_0)$, so there is no model $M'\models PA$ such that $M'$ is end extension of $M$.