Is there ANY WAY that I can use PHP to automatically fill in a form on another website than my own?

Currently, the user submits data to me, which is stored in a DB. If they want the data to appear on another site, they must then type it into the other site.

I was thinking of building a form where the user types the data into it, it runs off and submits it elsewhere and then the confirmation page of the other site pops up.

Any ideas?