We do this, albeit in a slightly hacky way. Here are the steps:
- Generate the PDF with FPDF and save it to a location on disk
- On the page that has loaded (or from another page) we have an iframe. With JavaScript we set the frame's location to that of the PDF
- Again use JavaScript to print the iframe.
Note: our method has us confirm the print dialogue button before it prints. This is possibly something you can set with your printer settings.
If you want to just print without that hassle, there are ways to directly connect to your printer from PHP, but the only one I know of is via a PECL extension, and I think that's Windows only.