The hyphenated follow-up does not work as a verb. It has two uses: (1) as a phrasal adjective meaning following or building upon an earlier event, and (2) as a noun meaning the act or instance of following up or one that follows.
These writers use follow-up well:
A follow-up call from the mayor’s office asked whether they would host an event. [Columbus Dispatch]
The G2 is the follow-up to 2008′s G1, the first phone based on Google’s Android operating system … [WSJ Digits]
The one-word followup is increasingly used in place of follow-up, but most major publications still use the hyphenated form.
Follow up, with no hyphen, is a phrasal verb and hence is two unhyphenated words. In these examples, followup and follow-up would bear replacement with the two-word follow up:
Each time Morecraft would stifle the attack, he would follow-up with a torrent of ground punishment … [Canton Journal]
And we recently asked reporter Ashley Milne-Tyte to followup with some advice for how to improve your chances of success. [qtd. by Marketplace]
I will follow-up with a post highlighting your ideas. [Big Think]
