This is an excellent question!
A lactating woman can have a mammogram; as a matter of fact, it is during this time that an annual mammogram becomes even more important because lactation can make small lumps harder to detect during routine breast self-exams.
Lactating breasts can make it more difficult to read the mammogram’s results because milk production causes the breast tissue to become denser. It’s recommended that women nurse just before their mammograms to empty their breasts, or even request a radiologist who specializes in reading the x-rays of lactating women.
Due to increased tenderness and sensitivity, mammograms may be slightly more painful for nursing women, but the x-rays are perfectly safe and do not harm the quality of breast milk.
So, not only is it perfectly fine to have a mammogram during lactation, it is highly recommended. Your wife should definitely keep her scheduled mammograms, even while enjoying a healthy ANR!