My mother-in-law lives with us going on 5 years. She is 93 and has dementia, diagnosed Alzheimer's. She can't remember anything even 30 seconds after it happens. Otherwise, she is in good health in her body. Better health than we are even. It will be a big change for her to live someplace else so we thought if we bring the subject up often, show her the facility, let her know we are so tired and can't do this, etc. then something will register in her mind and it won't be as much of a traumatic change. Is it worth trying or a waste of effort?
That said, start touring places by yourself within a geographic area that you deem reasonable. Narrow down the list to 2-3 places, and then tour them with your husband. Write up pros and cons for each, and help your husband make the best choice for your MIL to live. Here is a snippet from one of the best answers I've ever read:
"...gently make clear that this is how it will be now. It is, as with very young children, best not to give choices when choices are confusing and frustrating. It is best to gently say what will now happen. Don't expect a good response. Expect an honest one. Which will be grief. There are times when grief is a fact that cannot be avoided for you all..."
But I think it's worth a try. A test-run, so to speak, to see how she reacts and before any major changes occur. Maybe just take her to the facility for a tour at first. She how she does. This might give you a better idea of how to approach discussing the subject with her. Being at the facility is a visual, something she can see and hear and touch and feel. It might make more of an impression at first than trying to discuss it with her first especially since her recall is so poor.