Plugin: File Upload
Plugin add new form brick - File Upload, you can optionally add it to signup or profile form at aMember CP -> Configuration -> Forms Editor User can upload some file here
Then admin can see list of uploaded files in user edit screen in admin interface in tab Uploaded Files. Admin can upload files on user behalf here.
You can enable email notification for admin once user uploaded new file. aMember CP -> Configuration -> Setup/Configuration -> File Upload
Plugin add new advanced user search criteria - Misc::Have uploaded at least 1 file
You can download uploaded files all at once aMember CP -> Users -> Browse Users use Advanced Search to choose desired group of user and then click link 'Download Files (.zip)' below table with users on right hand side.
Optionally you can add widget with user uploaded files to his dashboard