As for the matter of marrying her, you ask whether it is lawful for you to wed her now that he has stepped aside.
If he has truly withdrawn and no longer wishes to marry her, then there is no objection to your marrying her.
However, if he still desires her and only gave up the engagement, as you said, out of shyness or social courtesy, then it is better that you leave the way open for him to marry her.

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Deserting One’s Wife

Question: A man abandoned his wife for two full years. He neither divorced her nor restored her to her children, nor did he provide the obligatory maintenance. She has no relative or anyone else to support her, so her condition is extremely difficult and painful; she is cut off from everyone except Allah. What is the Islamic ruling on a husband who leaves his wife—the mother of his children—to such a wretched and distressing fate?

Answer: There is no doubt that a wife has rights over her husband that he is duty-bound to fulfill. Allah the Exalted says, “And they (the women) have rights similar to the obligations upon them, according to what is just.” ⦗Al-Baqarah 2:228⦘. The Prophet (peace and blessings be upon him) said, “Your wives have a right over you.” Allah also says, “Live with them honorably.” ⦗Al-Nisāʼ 4:19⦘, and, “Either keep them in an honorable manner or release them with kindness.” ⦗Al-Baqarah 2:229⦘, and there are many other evidences obliging the husband to fear Allah concerning his wife, to give her her dues, and not to withhold any of her rights without a valid Islamic justification.
If she is defiant (nāshiz) and what you have mentioned