For my work email I use K9 email app. For the incoming, I use the POP3 server from my work (pop3.work.net) but for outgoing I have to use my home ISP's server (outgoing.verizon.net). Also, make sure you check the details on each because they sometimes use specific ports and have specific security requirements for each.
Its a weird combo but I've seen similar issues with servers not allowing outgoing mail originating outside the server.