First and foremost, he should remember this: he is not obligated to sacrifice his own health, his job, and his future retirement simply because social services imply that “the family has to manage on its own.” A caregiver can refuse to take on this role if it has become too much to handle.
From what you describe, the problem has already gone beyond what one person can handle in the long term. If, because of caregiving, he isn’t sleeping, isn’t working, and can’t support himself financially, this is not a sustainable situation.
I would advise insisting on a full assessment of both parents’ needs, not just the mother’s. If the father also needs help, it’s surprising that they’re trying to treat this separately. It’s also worth asking about respite care, day centers, and the possibility of increasing the home care package.
As for support it would be very helpful for him to talk to other people in the same situation. Often, it is on caregiver forums that you can get practical advice on social services, funding, and how to advocate for your rights.
Most importantly: if he is already physically, emotionally, and financially exhausted after a few months, it does not mean he is weak. It means that the system is currently relying on one person more than it should.