The requirements and steps:
1) BACKUP and Install on the J3.x website.
2) Make sure the old F2C J1.5 database tables are present in the new database. (They should have a different database prefix!!)
3) If you don't want the imported data to have wrong relations to the new make sure your current user IDs, access and view levels and group IDs are the same. (because these are variables in your old Joomla articles). This works out if you have a clean J3.x version and use a import component that retains the IDs of the old website:
4) The categories don't need to have the same IDs but require the same "alias".
5) MIGRATE: In the migration component set the prefix of the old tables and run the import
6) Via FTP migrate all files from <root>/media/com_form2content/ AND <root>/images/stories/com_form2content
7) Open the F2C Content Type and check (new) settings.
8) If you imported the Joomla articles also (with the Joomla migration component) and now run F2C you will get all your articles double and the new ones will have an alias with version number. To overcome this remove (and empty trash) the Joomla articles that have previously been written by F2C on the J1.5 website.
9) Now TEST run by opening ONE article in F2C back-end and saving it. If all goes well a new Joomla article will be generated. If so you can batch refresh all other articles. I would suggest making checks on ID settings and location etc. to know for sure all is goin well.