For Office 365 get information about the ownership for Office 365 groups of a user, given by the mail address. Using this script needs the cmdlets for AzureAD (https://docs.microsoft.com/de-de/azure/active-directory/users-groups-roles/groups-settings-v2-cmdlets).

GetGroupOwnership.ps1

param (
    [string]$UserMail
)

function Ensure-AzureADConnection
{
    try 
    { 
        # $var = Get-AzureADTenantDetail 
        $var = Get-AzureADUser -Top 1
    } 
    catch [Microsoft.Open.Azure.AD.CommonLibrary.AadNeedAuthenticationException] 
    { 
        Write-Host "You are not connected to Azure Active Directory."
        
        $c = Connect-AzureAD -credential $cred 

        if ($c -ne $null)
        {
            $account = $c.Account
            $tenant = $c.TenantDomain

            Write-Host "Connected as $account to $tenant"
            Write-Host
        }
    }
}

Ensure-AzureADConnection

$output = @()

$filter = "startswith(mail, '$UserMail')"

$user = Get-AzureADUser -Filter $filter

if ($user -eq $null)
{
    Write-Host -ForegroundColor Red "User with mail address $UserMail not found"

    Quit
}

$userObjectId = $user.ObjectId

Try
{
    $groups = $user | Get-AzureADUserMembership -ErrorAction SilentlyContinue
    $count = $groups.Count
    
    Write-Host "User $UserMail is member in $count Office 365 groups."
    Write-Host
}
Catch
{
}

$hasOutput = $false

foreach ($group in $groups)
{
    $groupObjectId = $group.ObjectId
    $groupOwners = Get-AzureADGroupOwner -ObjectId $groupObjectId

    $ownerCount = $groupOwners.Count
    $isOwner = ($groupOwners | Where { $_.ObjectId -eq $userObjectId }).Count -gt 0

    if ($isOwner -eq $true)
    {
        $hasOutput = $true

        $element = New-Object PSCustomObject
        $element | Add-Member -type NoteProperty -name DisplayName -Value $group.DisplayName
        $element | Add-Member -type NoteProperty -name ObjectId -Value $group.ObjectId
        # $element | Add-Member -type NoteProperty -name Description -Value $group.Description
        $element | Add-Member -type NoteProperty -name OwnerCount -Value $ownerCount

        $output += $element
    }
}

if ($hasOutput -eq $true)
{
    Write-Host "User $UserMail is owner in the following groups:"
    
    $output | Format-Table
}