If you are working in hybrid environment , did you try sync on-promise distribution group to Office 365 using Azure AD Connect ?
Please don't forget to mark helpful reply as answer
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I want the on premise distribution group to communicate with a group on exchange online
If you are working in hybrid environment , did you try sync on-promise distribution group to Office 365 using Azure AD Connect ?
Please don't forget to mark helpful reply as answer
You have a set of DLs on-premises, and you now want to move them to Exchange Online without changing any of the members. You don't want to create new Office 365 Groups based on the DLs; you want to use them as they are.
Do you have a hybrid environment? If so, you can use AADConnect to synchronize the on-premises DLs with AAD so that they appear in the cloud GAL. The groups will have to be managed on-premises because they are "owned" by that environment.
If you don't want to synchronize the groups, you can recreate the DLs in the cloud. It's easy enough to use PowerShell to export DL membership to something like a CSV file (on-premises) and then read that CSV file to create the DL in the cloud.