If she takes the betta out of the five gallon and keeps the snail in there, do the regular water changes in it, probably still a little more than normal and check that water quality with a test kit to see if anything is off.
Is the tank cycled?
If not, use Prime water conditioner, it gets rid of the toxic levels of ammonia/nitrites/nitrates.
If it is cycled, then nevermind, but Prime is still good to use.
It doesn't get rid of water changes though.
I don't know how a tank works using a filter and not cycling the tank, so I can't say anything there.
But I know Prime will help keep the water safer and just keep up with water changes and checking the water quality.
If everything is okay after testing the water and fixing anything with water changes, he should be okay to put back in once he's better!