Site Mailbox

Starting March 2017 you will see the following message when trying to add a site mailbox to your SharePoint Online site

This is due to the fact that the site mailbox feature in SharePoint Online starts being deprecated beginning in March, 2017. New SharePoint Online tenants have no access to the site mailbox feature and existing SharePoint Online tenants can no longer create new site mailboxes, which results in the message above.

All previously created site mailboxes are still accessible and will continue to function, however, the site mailbox feature is planned to be removed entirely in a future release.

The official announcement can be found here:

Other options

As per the above-mentioned announcement, there should be a migration tool available around September, 2017, but already consider other mail exchange solutions, such as Office 365 Groups and Shared Mailboxes. 

Office 365 Groups

Office 365 Groups are a great mixture of SharePoint and Exchange capabilities, with site collection created in the background and a mailbox associated with the group. You can see that with Powershell:
# Connect to SPO and EXO
Connect-SPOService -Url
$sesja=new-pssession -configurationname -connectionuri "" -credential $credy -authentication basic -allowredirection
Import-PSSession $sesja

#Check the SharePoint site

#Check the mailbox associated with the Office 365 Group:
Get-Mailbox -GroupMailbox

Shared Mailbox 

Shared mailboxes do not require a separate license and offer up to 50GB of storage space.  You can create them via Powershell:
New-Mailbox -Name "Shared Mailbox" -Shared

 or Office 365 Admin Portal by navigating to Groups>Shared Mailboxes:

More information on Shared Mailboxes is available here: 

Other Languages

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SharePoint Online: Nie można już tworzyć nowych skrzynek pocztowych witryn (pl-PL)