After completing her Ḥajj rituals on behalf of herself, this woman should go outside the boundaries of the Haram in any location, such as Taneem, and there she can initiate the intention (niyyah) for ῾Umrah on behalf of her deceased husband.
This is similar to what Lady ῾Aā᾽ishah (may Allāh be pleased with her) did. She had performed Ḥajj Qirān (combining Ḥajj and ῾Umrah) but wished to perform a separate ῾Umrah as the other women did who had performed Tamattu῾ (performing ῾Umrah followed by Ḥajj).
Ibn al-Qayyim explained this situation: “She had initially intended ῾Umrah but began menstruating. The Prophet (peace be upon him) instructed her to combine her Ḥajj with her ῾Umrah, making her a Qārin (one performing Ḥajj Qirān). He informed her that her Ṭawāf around the Ka῾bah and her Sa῾iy between Ṣafā and Marwah would count for both her Ḥajj and ῾Umrah. However, she felt discontented that her companions were returning with both a separate Ḥajj and ῾Umrah since they had performed Tamattu῾ without menstruating or combining, while she would return with an ῾Umrah within her Ḥajj. So, the Prophet (peace be upon him) ordered her brother to take her to Taneem to perform a separate ῾Umrah to soothe her heart.”
Ṭāwūs narrated from ῾Aā᾽ishah that she had intended ῾Umrah, but upon arriving in Mecca, she did not perform Ṭawāf because she began menstruating. She performed all the rituals of Ḥajj after intending Ḥajj. On the Day of Sacrifice (Yawm al-Naḥr), the Prophet (peace be upon him) told her: “Your Ṭawāf is sufficient for your Ḥajj and ῾Umrah.” However, she insisted on performing a separate ῾Umrah, so the Prophet sent her with her brother ῾Abdul-Raḥmān to Taneem, where she intended to perform ῾Umrah after she has performed Ḥajj.
Regarding your question about her being treated like a resident of Mecca: Residents of Mecca, when intending to perform ῾Umrah, must go outside the Haram boundaries to enter ᾽Iḥrām and then initiate ῾Umrah from there. They do not enter ᾽Iḥrām from their homes as they would for Ḥajj.
Fatwā issued by Dr. Khālid Naṣr