if you setup new module like old module in settings of the Module, you can skip transferring data from Modules, TabModules, ModuleSettings, TabModuleSettings and ModulePermissions tables. while in settings, notice the moduleID (or MID) parameter in URL.
Next copy over all items from FAQsCategory and next from FAQs table, adjusting moduleID accordingly. For this purpose use SQL statements like
INSERT INTO newdb.FAQs ([ModuleID], [CreatedByUser], [CreatedDate], [Question], [Answer], [CategoryId], [DateModified], [ViewCount])
SELECT ({newmoduleID}, CreatedByUser, CreatedDate, Question, Answer, CategoryId, DateModified, ViewCount) FROM olddb.FAQs WHERE ModuleID = {oldModuleID}