The winmail.dat problem exists as mail sent from Microsoft in RTF (Rich Text) can’t be translated when received on the incoming server.  The method of sending rich text is called Transport Neutral Encapsulation Format (TNEF).  To resolve, set the REMOTEDomain‘s TNEFEnabled property to false.  To do this, we need PowerShell.

1. Open PowerShell as an Administrator.  Then run:
   New-item –type file –force $profile
2. Then:
   notepad $profile
3. Then, paste this into the notepad window, change ADMIN-EMAIL to your administrator account, then close and save it.
   Function Connect-EXOnline{

   $credentials = Get-Credential -Credential ADMIN-EMAIL
   Write-Output "Getting the Exchange Online cmdlets"
   $Session = New-PSSession -ConnectionUri https://outlook.office365.com/powershell-liveid/ `
   -ConfigurationName Microsoft.Exchange -Credential $credentials `
   -Authentication Basic -AllowRedirection
   Import-PSSession $Session
   
    }

4. Then close PowerShell and open it again as an Administrator.  Then run:
   Connect-ExOnline
5. You should be prompted for your credentials.
6. Run this cmd:
   Set-RemoteDomain Default -TNEFEnabled $false

You can check the RemoteDomain policy with this cmd.  Look for the -TNEFEnabled flag.

Get-RemoteDomain | fl *