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gives the impression that it's anothers website?
Perhaps the reason the other websites PDF's are not indexed by google is because the site doesn't desire them to be indexed. (My own PDF's are stored in an image folder and excluded in robots.text. Anybody who begins crawling them is denied access.)
PDF's come in a variety of formats (text and/or image).
I archive some both ways. It's really dependent upon what I'm attemtping to accomplish.
Text saved as a PDF image is generally not searchable.
Best solution that you may have is to download all the PDF's from the "others" website and search them offline. There are many tools for this.