There are two methods for upgrading Distributed Groups to Office 365 Groups. One has to be an Office 365 global admin or Exchange admin for performing the upgrade using either method.
Using the Exchange Admin Center:
A global admin can access the controls in the Exchange Admin Center.
Select Receipts and then Groups. The eligible Distribution Groups will be available in the list that appears.
Click on the Upgrade icon and confirm the dialog box to begin the process.
It is possible to upgrade multiple Distribution Lists simultaneously by selecting the appropriate ones from the drop-down list of eligible Distributions Lists.
Microsoft has provided PowerShell scripts for upgrading Distributed Groups to Office 365 Groups using different cmdlets.
If there is only one Distribution List to upgrade, it can be done either with the Upgrade-DistributionGroup cmdlet or New-UnifiedGroup cmdlet. The New-UnifiedGroup cmdlet applies only to Exchange Online.
The syntax for Upgrade-DistributionGroup cmdlet looks as follows:
Upgrade-DistributionGroup –DlIdentities, < Distribution List 2 SMTP address>, < Distribution List 3 SMTP address>, …where the Distribution List SMTP address is the shared email address available. Create an mail with the help of experts.
Factors to Consider When You Migrate Groups to Office 365:
At present, it is only possible to migrate cloud-based, non-nested Distributed Groups to Office 365 Groups. In other words, a Distribution Group created and managed with on-premises Exchange cannot be upgraded to Office 365 Groups directly. There are other restrictions on lists as well. Dynamic Distribution lists and security groups cannot be migrated. Also, Distribution Lists with either no owner or over 100 owners cannot be upgraded. It is possible to check if a Distribution List is eligible for an upgrade by using PowerShell script. Know more about Office 365 to Office 365 migration in detail.
I hope this information will be helpful!