Using an avatar selected in one Module through a series of modules

Good day. 

I'm creating a series of modules that form part of one course. The client wants the user to be able to select from a bank of 6 avatars to represent themselves in each module. The issue is that each of the 5 modules will be separate SCORM packages, uploaded separately onto the LMS. That means that the user will need to select an avatar each time they open a new module.

Is there a way to have the user select their avatar once, and have that selected avatar appear through all the different modules (without having to re-select it each time they open a new module)?