When a user registered a website in a multi-site network and he can log in to all websites in the network. The plugin User Role Sync is able to help multi-site user to realize it.
Multisite User Role Sync works as follows:
When a user visits a website, the plugin will check whether the user is a registered user.
If this user is already a registered user, no action will be taken.
If the user is not a registered user of this site, add the user to this site (automatically assigned the role you set the default role – [synchronization roles]
If this user is not a registered user of blog, this user will be assigned the specified default role [default role]
When a user’s role is updated, this user’s role in all blogs can be updated. 【Role Update】
Search Multisite User Role Sync at the backend, you can install the plugin or downloaded here https://wordpress.org/plugins/multisite-user-role-sync/, unzipped and uploaded to wp-content / plugins directory to install.