Import a PDF and preserve ligatures

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My suggestion would be to use the excellent Pandoc to convert your LaTeX file into an ODT.

Ligatures (as I understand it) depend on the font's encoding and capabilities. If you use something like Khaled Hosny's superb Libertinus fonts (tweaked versions of Linux Libertine and Biolinum), your ligatures will "automatically" work in LibreOffice Writer. There are, of course, other font options if you prefer.

(The bug report you linked in the comment to your question is a very old one, and open type features have been working nicely in Writer for some time now.)

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If I pick a XeTeX generated PDF with text containing ligatures and open it on a PDF viewer (I use Okular), select some text, copy and paste on Writer, the ligatures are copied without problems, but that's because the original document uses OpenType fonts. If the PDF was generated using LaTeX and metafont, conversion would not be that easy.

Generally speaking, converting PDF to anything is a bad idea, so you need to either translate the original .tex file to .odt as suggested by @David or recreate the whole document from scratch on Writer: any other option would be too much work.