Yep that will be possible.
Step 1: Exporting Module
Right click the → Select Export Module Package , from the module which you want to Export from your source project
You get a Warning dialog message like above incase you have usage of this module with others,
Step 2: Click Continue Exporting and click next step for Dependencies conformation
Step 3: Select the file location where you want store you .mpk file and click Save
in few seconds export will get done. And confirm with file location whether the .mpk file is available or not
Step 4: Open your Destination application which means 9.6.9 in your scenario
Step 5: Right click In main module in project Explorer and select Import Module Package
Step 6: Select the .mpk file which is exported from your 9.10.1
Note: It may raise some error due to usage in previous application we have to fix them.
I hope it will help you let me know incase you have any support.