I wonder if there is a simple way to download and save a pdf from a website and then upload the same file to another website through an HTML5 form.
When you view the PDF on the website in Safari, press the "share" icon and then select "Save to Files". Now store the PDF document, for example on iCloud Drive.
Then browse the second website and click the button to upload a file. You will be asked then if you want to take a photo, access your photo library or "Browse". Choose "Browse" and you'll be able to select the PDF document, you've saved earlier.