What is the best way to tell if a mailbox has been succesfully provisioned in Office365?

If you are using AADConnect to sync from on-prem to ExO, thats expected. It can take up to 30 minutes to sync unless you do a manual delta sync.

If you want to simply make sure the mailbox exists in 365, get-mailbox <user> will return that object when connecting to Exchange Online via Powershell.

Unless you are thinking you need to check something else to verify the license.

If so, then:

Get-MsolUser -UserPrincipalName <user account UPN> | Format-List DisplayName,Licenses
Get-MsolUser -UserPrincipalName <user account UPN> | Format-List DisplayName,Licenses

https://video2.skills-academy.com/en-us/microsoft-365/enterprise/view-account-license-and-service-details-with-microsoft-365-powershell?view=o365-worldwide

You really need to look at both the Azure and EXo accounts if you want to be thorough :)

One easy way to tell is if the ProxyAddresses on the Msol side match the Email Addresses on the ExO side.

All the Azure ProxyAddresses should be contained in the mailbox. ( not the other way around)
If that is the case, you know its synced up.

You could also look at modified times on each object, but they wont not typically match as their a delay sometimes.

I dont put a lot of weight on OverallProvisioningStatus. I have seen that not show "success" many times on accounts that are just fine.

P.S. I should add that if the mailbox exists in Exchange Online, that's typically all that is needed and you should be able to modify. At times, there is a delay or issues between the AzureAD and Exchange Online sync, but, for the most part, if the mailbox exists in ExO, you are good to go and any modifications you make will be reflected at some point if there is an issue.

As far As I know, you could assign license to mailbox directly when this account show in Azure AD. So, you can check whether the account appears successfully, then assign license to it(You can also create loop which check every 1 minute):

$data = Get-MsolUser -UserPrincipalName User1@domain.com -erroraction 'silentlycontinue'  
if ($data -ne $null){  
[Assign license Action][1]  
}  
else{  
write-host "Try again later"  
}  

About other action, due to remote mailbox's AD account is hosted on local AD, so you need to modify it from local AD rather than Azure AD. You can modify local account at any time, regardless of whether the account is synchronized, because the modify action will synchronized later.

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