Is it possible to automate emailing downloads?

I have a new cloud-based accounting software that includes a nifty option of emailing a file to a set email address and it stores any attachments which I can then process accordingly. This is great for bills I'm emailed as I can just forward the bill on and it appears there when I'm ready to process it.

But some companies I have to log on online and then download the file. Previously I'd save it locally but now I'd like to forward it on automatically if possible?

I always make sure my downloads are set to ask what to do with the file - ie open or save as ... but now I'd like to add a third option if possible, open, save as or email. As far as I know no browser does that by default. Is it possible to make a browser do that? Possibly by an add-on or something else? Anyone else come across anything like this before? My Google-fu is not helping here.