Replacing a joist that's sitting on a brick footer

House is a 1920 Dutch Colonial.

Over the years the floor in the florida room (single story room, 9x13, sits on the south end of the house) has started to lean on one side (the short 9' side). I never paid much attention to it as nothing is in that room except a desk and a chair. Yesterday I looked down there and it looks like the joist that sits on the brick footing has some rot, causing the sag. The footer is 2 bricks thick and sits on top of a concrete wall that is 8' high (which is the wall of the basement).

What would be the best way to repair this?

I was going to get a floor jack this weekend and get it in then slowly jackup up the floor to make it level. Or should I do that then, once done, remove that joist or sister one to it?

At one time there were some water issues in that area but they've since been resolved.