Is it fine to do a "rewrite" of an old fic made by someone else?

there's this fic I absolutely love, but unfortunately, the last update was a couple years ago (2020 or 2021 i believe) and it doesn't seem like the author is active on the site anymore.

naturally, i've decided to take on the mantle of taking the whole fic and rewriting it, as well as possibly continuing it on and (hopefully) finishing it

is this alright to do? should i PM the original author first or is just linking the original work and explaining my reasoning enough?