Assuming your ebooks are in epub format you can use a free program called Calibre to convert them to mobi or azw3 format for your Kindle. You can download Calibre here:
https://calibre-ebook.com/download
Download and install the one for your computer and drag the book into the main window of Calibre and click Convert and select mobi or azw3 to convert to. I use mobi. Most of those in here use azw3 which is a more advanced format and gives you additional features. Connect your Paperwhite to your computer and tell Calibre to put the book on your computer. That's it.
You can also do bulk processing, dragging a lot of books into Calibre, selecting them all and clicking convert. Then tell Calibre to put them on your Kindle.
This is the barebones method and it assumes you don't have any DRM on your books. If you're reading them in FBreader I'm guessing you don't although I don't know FBreader well enough to be sure of that. If so, there are plugins to deal with that.
Once you're comfortable with this you might want to look into the various ways you can improve the text with other fonts or adding covers or metadata or whatever you like. Calibre can do a LOT. But for simply converting formats it's pretty simple to use.
Barry