Is it permissible for a husband to initiate conversations with a non-mahram woman via social media and continue talking to her under the pretext of offering advice or inquiring about her health, knowing that he had previously agreed with his wife that neither of them would talk to the opposite sex?

It is advised not to seek divorce for the reason mentioned. Instead, one should reach an understanding with the husband and live with him righteously. Divorce is not a light matter, and a minor mistake does not justify destroying the family. One should be gentle with the husband and cooperate with him in obeying Allah, avoiding disobedience, and closing the doors to tribulations, all while thinking well of him and being wary of spying and excessive jealousy.