Migrating to Office 365 and DL

We are in the process of migrating all of our users to 365 and last week complete moving all 12K+ users to the could which included recreating all DL in Office 365.  After getting a large number of calls about users not being able to receive emails from outside sources and other delivery problems, manage request we recreate all DL onprem again and remove them from the cloud as to stabilize the environment until a better action place on move forward was found. What is the best and safest way to slowing move all onprem DL's to Office 365?  I have ready of that you can create a DL or contact onprem and point this to the out DL in someway. What are all of our options?
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John ChumaCommented:
How did you migrate the mailboxes and DLs to O365?

Are you using AD Sync?

Did you cut over the MX records over to o365?
compdigit44Author Commented:
You use a script provided to use by our MS resource that would inventory our onprem DL and recreate the in the could which did work. We are using AD Sync and our MX record still points onprem and management has been hesitant on giving up the OK to change the MX record to point to office 365
Ajit SinghCommented:
You may consider Exchange Server Deployment Assistance a web based application just you have to select what kind of deployment you were interested and then its provide you step-wise instructions to get this job done: https://technet.microsoft.com/en-us/office/dn756393.aspx

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