And I'm now requested to use a pre-existing .PDF file and this plug-in "Form Generating PDF - Wordpress plugin" https://codecanyon.net/item/form-generating-pdf-wordpress-plugin/20403948 to export the form to PDF . So it's not "generating PDF file" now, it's "injecting data into an existing PDF file".
This plugin will send an PDF attachment filled with form user data, via email after his registration on a form, it's easy and manageable in simple three steps, it has the most unique features, that cannot be found on any existing plugin on the market.
(We don't need to send e-mail, just download the PDF, but the plug-in also says it does that.)
Some more research: I've read that I could use FPDI ( https://www.setasign.com/products/fpdi/about ) and FPDF ( http://www.fpdf.org/ ) to inject data into and existing PDF with PHP. Both are indeed user by the plug-in. Not sure if I better start something from scratch or retroengineer the plug-in to some extent and find some shortcut. Hints and solutions still welcome.