Cloning O365 Group Memberships

That depends on the specifics I guess. Here's a quick sample of what you can do with PowerShell.

List all groups a given user is a member of:

$dn = (Get-Mailbox user).DistinguishedName
Get-Recipient -Filter "Members -eq '$dn'"

Use the above list to add another user as member:

Get-Recipient -Filter "Members -eq '$dn'" | % { Add-DistributionGroupMember $_.Name -Member anotheruser}

That's a really basic code though and it assumes that all the groups are distribution ones. A bit more complex one will check the actual type and use the corresponding cmdlet:

$dn = (Get-Mailbox user).DistinguishedName

Get-Recipient -Filter "Members -eq '$dn'" -RecipientTypeDetails GroupMailbox | % { Add-UnifiedGroupLinks $_.Name -LinkType Member -Links anotheruser }

Get-Recipient -Filter "Members -eq '$dn'" -RecipientTypeDetails MailUniversalDistributionGroup | % { Add-DistributionGroupMember $_.Name -Member anotheruser }