How do I retrain a cat to use the litterbox I prefer?

Given the cat's owner is going away for sometime, it's entirely possible for you to train the cat, but time and patience is key.

Start by using a shallow tray type litter box and keep it in the showers. Once she is in the routine of using it, you can move it out of the shower and place it next to the shower.

Bit by bit you can gradually move the litter box.

I'd recommend not complicating the issue by using a deep litter tray or one with a roof. The cat needs easy access to it and for it to be apparent that is has "diggable" substance in it, conducive to burying waste.

I personally feel like there's a good chance this will not go well at all for you. Cats are highly territorial, and so transplanting to a whole new space will be very stressful, which can lead to litterbox problems on its own. Furthermore, the cat is quite old, and older animals tend to not deal with change and stress as well as young animals.

The other concern I have is that there's a decent chance the cat doesn't necessarily think shower = where it should eliminate. It might think that particular room is where it should eliminate, but doesn't necessarily generalize that to other bathrooms. Given nothing familiar, it may very well pick any of your rooms as its new spot. It would be an easier task to retrain the cat to use a litterbox in the space its already used to. Then you could start by placing a large lid-less litterbox in the shower, so that it will have no choice but to use that, and then try to very gradually move the box to a more convenient location.

Lastly, you should be aware that cat urine in particular is extremely difficult to fully clean. Even if you think it is clean, the likelihood is that residue is still there, unless you went out of your way to make absolutely sure it is clean. Your friend's bathroom is likely very unsanitary from years of having a cat urinate in it. It is never recommended to simply allow the cat to use anything other than a litterbox.

If I were you, I would try to care for the animal in your friend's home instead. If your friend is concerned about the cat being alone so long, you might even consider offering to just live there and housesit while they are gone.

Cats learn their entire life, so please do not worry about the litterbox. Most likely you will only need to show her the litterbox and how to dig a little.

To show her how to dig, you simply put the cat onto the litter and take her paw and dig a little. You will need to take the lid off the litterbox and leave if/or until she understands what you want.

The thing you want to do is to put the litterbox in a quiet place of your house, so she can do her stuff undisturbed.

If the cat has problems finding the new litterbox, she will let you know. You might want to leave the lid off the litterbox for the first day or so, until she starts to use it.

It might be best if you close the shower or she might use it, I find it strange that the owner lets her use the shower as a toilet.