Copy one user's AD groups to another user

I am trying to copy 1 users AD Security Groups to a 2nd user I created via PowerShell. I know I could copy the user from ADUC but I am trying to do this with PowerShell. The user I am trying to copy has 8 groups and I will need to create multiple users with the same permissions so any help would be appreciated since this will save me considerable time and prevent accidentally adding the incorrect groups.

$User = "user1@domain.com"
$UserAddingGroups = "user2@domain.com"
Get-ADUser -LDAPFilter "(&(UserPrincipalName=$User))" -Properties * | Select-Object MemberOf | 
   ForEach-Object { $_.MemberOf | Add-ADGroupMember -Identity $_.MemberOf -Members $UserAddingGroups -Confirm:$true }

I can get the list of groups by typing a variation of the above, so I think I am close.

Get-ADUser -LDAPFilter "(&(UserPrincipalName=$user))" -Properties * | Select-Object MemberOf | 
   ForEach-Object { $_.MemberOf | Format-Table }