Are you familiar with FileMaker scripting?
There's a script step, send mail, that can do what you describe if you have a compatible email client program installed or it can use an SMTP email server.
I'm not but work with someone who does. Will any outgoing smtp server work then? Even if the incoming is POP?
I haven't used SMTP. I just see that it's an option when setting up the send mail step in a script. From the posts made here, there are issues that can make SMTP a challenge and emails via SMTP may be automatically filtered out of in boxes by spam filters.
Even if the incoming is POP?
Since Filemaker can't natively receive email, only send it, I doubt that this matters.
For More Information on SMTP and Spam filters, see: Email header malformed when using SendMail
This is one of many acknowledged bugs that can be found in the Known Bug List here in the Report an Issue section of the forum.
It can also be downloaded as a database file from: http://www.4shared.com/file/8orL8apk/FMP_Bugs.html