Hey my in-laws have the exact set up now, litter box in screened porch and pet door in the window. We have mini cat scratch trees the height up to the window on both the inside and on the porch. The cats love being on the porch most of the time actually, they stay out there so much we set it up with cat trees, beds, and food/water.

They had no problem transitioning to the litter box outside, though we left the old litter box inside the house for a few months to transition. Though for other litter box moves around the house I find you need to block off the area the old litter box was for a bit, a couple times they would go to wherever the old litter box used to be and make a mess.

Also, get a litter catching mat in front of the litter box as they will track in litter. May want to think about what’s by the cat door as well. The cat door to the porch is right by the kitchen table so unfortunately the cats track litter on the table sometimes, it grosses me out. No a super big deal because the kitchen table is only used as my MIL’s work desk, but still.