Is it possible to move Google tasks from Gmail to Google Apps account?
Is there any way to export the Google tasks from my Gmail and import it in Google Apps account?
There's no way to export tasks. At best, you can email the task list to your Google Apps account and copy+paste, but again they become one big task instead of several, individual tasks.
There is now a great, free, third-party solution for this. It's still in beta and not quite perfect yet, but gets the job done. In addition, it can sync task lists between accounts on a regular schedule - finally a way to share Google Tasks with others!
A couple notes:
A huge thanks to herr.kaste for developing this!