This page is collection of powershell “oneliners” that I've used to migrate items from Office 365 tenant to another

Exporting classic distribution groups to .csv files

Connect-ExchangeOnline
Get-DistributionGroup -ResultSize Unlimited | Select-Object DisplayName,PrimarySmtpAddress,@{Name="EmailAddresses";Expression={$_.EmailAddresses | Where-Object {$_ -clike "smtp*"}}},RequireSenderAuthenticationEnabled | Export-Csv -Encoding UTF8 -NoTypeInformation C:\temp\exported_distributionlists.csv

And importing distribution lists. If importing another tenant, remember to clean onmicrosoft.com aliases and rename domains if needed.

Import-Csv C:\temp\distribution_list_export.csv | foreach {
$proxyaddresses = $_.EmailAddresses -split ' '
$managers = $_.ManagedBy -split ' '
New-DistributionGroup -Name $_.DisplayName -ManagedBy $managers -PrimarySmtpAddress $_.PrimarySmtpAddress -RequireSenderAuthenticationEnabled $_.RequireSenderAuthenticationEnabled -WhatIf
Set-DistributionGroup -Identity $_.DisplayName -EmailAddresses @{add= $proxyaddresses} -WhatIf
}

Exporting distribution lists members

Connect-ExchangeOnline
$objDistributionGroups = Get-DistributionGroup -ResultSize Unlimited
Foreach ($objDistributionGroup in $objDistributionGroups)
{
    write-host "Processing $($objDistributionGroup.DisplayName)..."
    #Get members of this group
    $objDGMembers = Get-DistributionGroupMember -Identity $($objDistributionGroup.PrimarySmtpAddress)
    write-host "Found $($objDGMembers.Count) members..."
    #Iterate through each member
    Foreach ($objMember in $objDGMembers)
    {
        Out-File -FilePath C:\temp\exported_distributiongroup_members.csv -InputObject "$($objDistributionGroup.DisplayName),$($objDistributionGroup.PrimarySMTPAddress),$($objMember.DisplayName),$($objMember.PrimarySMTPAddress),$($objMember.RecipientType)" -Encoding UTF8 -append
    }
}