Pulling content from another website

There is a website I link to a lot that has HTML documents that change now and then. However, links to some files keep failing ending up with broken links on my website. I was thinking of hosting these files myself but keep them updated when the site builds with the content from the source. Is this possible? (Alternatively, they provide a PDF document of any changes in the content and it may take a while for them to update those changes, so I can still see the changes made, but I was hoping to avoid doing the updates manually).