Error 'Sharing isn't available. Try again later.' on Salesforce Inbox

If a User hasn't yet connected their Email Account under Personal Settings
Connect the Email Account of the affected User under Personal Settings. Review Connect Your Email and Calendar to Salesforce with Einstein Activity Capture.

If the email doesn't contain any matching Contact or Lead email address in Salesforce
Create a Contact or Lead record in Salesforce that matches the email address on the email and wait for Einstein Activity Capture to auto-capture that email to Salesforce.

If the User has just connected their Email Account to Einstein Activity Capture and their account is currently on the initial capture stage
If an email account is already connected, you may try to reconnect it by disconnecting and reconnecting under the Einstein Section of Personal Settings. You must see a green banner above the Salesforce page with the message below as confirmation:
 

"We are getting Einstein Activity Capture ready for you. While you wait, choose who you want to share emails and events with."

Once done, the message on the side panel will show the following:

• Share with Everyone
• Don't Share
• Share with My Chatter Groups

The Log Email button will be replaced by one of the three messages above if the User has Einstein Activity Capture License assigned.