RE: Issue being faced with mailbox migration from Exc2010 to Office365.

Hi DineshSingh6800,

To narrow down the issue, could you try to use New-MoveRequest to check it?
Here are the PowerShell cmdlets to move one mailbox from on-premise to the cloud.
1). $RemoteCredential= Get-Credential
Then, type in the on-premise administrator credential in the prompt window.

2). New-MoveRequest -Identity “an on-premise mailbox” -Remote -RemoteHostName “mail.domain.com” -TargetDeliveryDomain domain.mail.onmicrosoft.com -RemoteCredential $RemoteCredential
Please note that the cmdlets above need to be run via the Exchange Online PowerShell.

After doing that, please use get-moverequest to view the status.
I have sent you a private message to request the information.
Here are the steps to access the private message.
 1. Please go to "Your details" section on the right side of the community site.
 2. Click Private Messages.
 3. Click the subject title to read the message.

Thanks,
Jason Jiang