I import everything into Calibre and then export files onto my Kindle from Calibre, too, so I don't know how you get mobi fics you download onto your hard drive from the DL folder or AO3 or wherever, over to your Kindle. Can someone tell me, please? Thanks!
If you're interested in simply converting from one format to another and then just adding that file to your e-reader, this
converter might do the trick for you.
If you want software that converts and manages your e-book/e-fic collection regardless of type of reader,
Calibre might be a program that would be useful.