There is a couple of issues here, Solmaz, one is browser based, the other is author based. The browser base is that most browsers today will either automatically open or auto download PDFs, but not both at the same time. This depends on how Users set their browsers up and there is nothing you can do about that.
The other is how the author has written it. If it is an interactive PDF, that is has fields in which students edit the answers in the textboxes provided, checkboxes, radio boxes, whatever, then it is a matter of educating the User to ensure they are downloading the document, editing it in Acrobat and not trying to edit it in their browser.
If it is an assignment that does not need to be downloaded, edited and uploaded, then why use the PDF format in the first place? Can it be an online assignment? Alternatively, can it be an uploaded response assignment.
Check with the author, make sure they are using the right format for what they need. I am not sure you can prevent a PDF from being downloaded under any circumstance, so why use the format if it is not to be downloaded? Much simpler to use a different format than trying to prevent a download, no matter what your LMS is.