BuddyPress.org

I haven’t figured out for profile header image yet, but you will find solutions for centralizing avatar storage on MULTIBLOG-enabled BP networks here: https://buddypress.org/support/topic/multiblogmultisite-avatar-missing/

Basically, if you want to use avatars from the main site, you can just add this to your wp-config.php:

define( 'BP_AVATAR_UPLOAD_PATH', dirname(__FILE__).'/wp-content/uploads' );                         define( 'BP_AVATAR_URL', '//'.$_SERVER['HTTP_HOST'].'/wp-content/uploads' );

If you want to use avatars from another site, you will likely need to add the site’s upload path (eg. ‘/sites/2’) to both paths.

There is a much easier way to sync avatars, directly from cPanel on the site, using command commands to sync avatars folder with other similar folders in subdomains or sub sites. Automated tasks (cron jobs) are set. This type of task is created in cPanel-> Automated tasks (Cron jobs), and through them you can specify in a certain period to perform an action.
For example, to sync the content of example.com/wp-content/uploads/avatars in sub1.example.com/wp-content/uploads/avatars, you can use the following cron task:
rsync -av –progress / home / directory of the site in cPanel / example.com / wp-content / uploads / avatars / sub1.example.com / wp-content / uploads / avatars /

It is recommended that cron tasks not be performed too often. You can configure the task to run every 10 minutes.

Here solution

After activating multisite I installed and network activated BuddyPress. I also added this line to wp-config.php: define ( 'BP_ROOT_BLOG', 2 ); where 2 is ID of your communitycommunity.mysite.com

That way BP is accessible from an entire network, but profiles are handled only from the network site.