Mom's closet is probably still full of her things, and Dad's shirts may be folded on a chair or stacked in a laundry basket because the hanging space never got sorted. You do not need to empty anything to fix this. You need to measure what he actually wears in a week and give that a home he can reach.
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Count the week first
Look at what he wore last week, not what he owns. Pull out the shirts, pants, socks, and one jacket he reaches for most. Those are the items that need the easy spots. Everything else, including the church suit, the winter coat, and the shirts he has not touched since spring, can move to a higher shelf or a bin marked for later. Count the outfits he really rotates. That number tells you how much hanging rod and drawer room he needs.
Fit the shelves to his reach
Put his daily items between his shoulders and his knees. If he has to stand on a stool to reach his undershirts, the system is not working. Check whether the drawers open fully, whether the rod is too high for him to slide a hanger off, and whether a bin is too heavy to lift from a shelf. A good fit is one where he can get dressed without thinking about where things are.
Keep the one-person rule
Give him his own side and label it with what he already calls things. Keep one shelf for the things he may want to talk about later, and leave the rest alone until he is ready. Ask him before you move anything of Mom's, and ask whether he wants a box set aside for you or the grandchildren. Taking it slowly is not wasted effort.
What to do tonight
Take one drawer. Pull out everything he wears in a week and put it on the bed. Put the everyday things back in the easiest drawer and the rest in a bag for the top shelf. Stop when you feel tired. The closet will still be there tomorrow, and he will have one drawer that works.
When to ask the doctor
If he cannot lift a bin, reach a shelf, or bend to a low drawer without pain or dizziness, mention it to his doctor. Ask what limits he should plan around. Then change the closet to fit those limits, such as moving everything to waist height and keeping the step stool out of his way.