Morally right? You need to examine the basic, fundamental meaning of morality. Morality is something that is life giving. Something that takes away life is immoral. Marriage is moral, in part, because it gives life to a new human being. It is expected that the parents are able to care for that new life; caring for the child is part of the same thing as giving it life. Anything that detracts from the parents ability to care for the child is immoral. In the same manner that serialization is immoral so would be not feeding it. Not rocket science.
So the dilemma. What immoral act do you do? If you have more kids you could die (always true) or be incapacitated. But giving life is good, denying it is immoral. Or, we can trust God. Could be your friend will never get pregnant again because it is God’s will. Or another child will be healthy and so will she. Sadly, most people do not talk to their priest about such matters. Priests often give good advice. Doctors are trained, and pretty much legally required, to warn people about the risks they may have if those risks are exceptional. What a sorry state that leaves people in. They fear.
I will tell you that the “official” Church says you have to have kids. You have to be open to life every time you have sex. I will also tell you that Catholics in the USA don’t average 12 kids anymore. Well, assuming married couples are having sex, likely, then something doesn’t add up. Any couple that doesn’t have a bunch of kids is probably sinning. Well, maybe not, but this site is not one that gets the individual choice part of Catholic teaching so all you will hear in this corner of the internet is that sterilization and the birth control that most Catholics are using is a mortal sin.
Realistically, your friend should be in a place where she thanks God for the children she has. And her marriage. She should seek out additional opinions about her health before she get pregnant or has a sterilization. But she should not be terrified of getting pregnant. Getting pregnant is supposed to be a joyous thing. Sex is supposed to be a joyful thing. Whatever she and her husband decide can be painful for them, you need to understand that. Whatever they do is a choice between them and God. It would be in very poor taste to criticize them no matter what they do. Maybe they really want more kids and the prospect of not having any more is very painful.
Having first hand experience in this matter I would say to pray and ask God what to do. I lean toward protecting the life that exists, and the love that exists, so I would not get pregnant. I would use a good form of birth control, something that works for my marriage, for awhile and have my medical condition re-evaluated in a year. Think of it this way, if God wants the couple to have more kids in that year her body will heal itself. If, in a year, the body has not healed then God is saying no more kids. At that time I think sterilization would be acceptable.
A family member’s uterus was hanging out of her after her second child was born. She had a hysterectomy. No more kids. Hysterectomies make childbirth impossible just like sterilization. I don’t think she committed a sin. But she could have waited and prayed for God to heal her, or had some sort of surgery to repair her uterus. It took them 5 years to get pregnant, so maybe she could of waited, done nothing for awhile.
What is really important is that your friend feels that she is doing the right thing with God. She should seek the advice of a priest to help her. Saying that, I talked to two priests about this subject and got two different answers. Some help. I am pretty sure a Bishop, or priest, would tell them not to get pregnant if it meant endangering somebody’s health. The difficult part is with sterilization, birth control or not having sex and the teaching of the Church to make sure that a baby in not conceived. My feeling is that once the decision has been made not to have more kids for moral reasons, there would be no sin in sterilization. Some reasonable senior, knowledgeable priests would agree with me, and do. Some priests don’t. But remember, this is between the couple and God, not you. We all need to be supportive.
Again, they need to praise God for what they have and be thankful.