You could try the process described here:
https://docs.moodle.org/dev/Moodle_2.7_release_notes#Assignment
I can't promise how well it will work, so it may be best to try it out on a copy of your site's DB + moodledata, rather than on the live site.
Assignment
Assignment 2.2 upgrading long after core upgraded to 2.8?
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