Is it permissible for a husband to ask his wife not to add men (whether non-mahram or relatives) to her email, knowing that she rarely uses their contacts and does not mind corresponding with them sometimes within the bounds of propriety, and the husband refuses this out of jealousy, considering that the marriage contract has been concluded but the wedding ceremonies have not yet taken place, and what is the way to convince her of this?

The general principle is that it is permissible for a man to address a non-mahram woman when there is a need, provided Islamic guidelines are observed. However, corresponding via email without a legitimate Islamic need is not permissible, as it opens the door to fitna (temptation/discord). The husband must prevent his wife from doing so with wisdom and gentleness, by informing her of the Islamic ruling, explaining the corrupting consequences that result from it, reminding her of the conduct of righteous women, and of the obedience to her husband that Allah has made obligatory upon her. As for her corresponding with her mahram relatives, it is permissible as long as it does not involve any forbidden Islamic act or lead to a corrupting consequence.