Q:

Copy Active Directory attribute to another attribute and modify it

I managed to copy an Attribute to another ("physicalDeliveryOfficeName" to "l"):
Get-ADUser -Filter '(sAMAccountName -eq "MyUserName")' -Properties l, physicalDeliveryOfficeName | ForEach-Object {Set-ADObject -Identity $_.DistinguishedName ` -Replace @{l=$($_.physicalDeliveryOfficeName)}}

But how can I manipulate the object before inserting it into the new attribute. 
Lets say:
physicalDeliveryOfficeName: "1234 City"
Now I want to remove the numbers and spaces before inserting it into the new attribute "l". 

A:

You simply would do that in your subexpression of your calculated property
$($_.physicalDeliveryOfficeName -replace '^\d+\s+')

That regex string will replace all leading digits (assuming there are not other characters at the start of the string) and all whitespace that follows it. 