Instead of processing a network share, try using invoke-command and run that portion of the script on the target server itself against the local drive letter.
$SAMname = "zPink.Panther"
$FullUserInfo = Get-ADUser -Filter "UserPrincipalName -eq '******@company.com'" -Properties SamAccountName,EmailAddress
$FullUser = ($FullUserInfo).SamAccountName
$ACLPathFull = "E:\Users\$SAMname"
invoke-command -ComputerName server-name -ScriptBlock {
$Rights = [System.Security.AccessControl.FileSystemRights]::FullControl
$Inherit = [System.Security.AccessControl.InheritanceFlags]::ContainerInherit -bor [System.Security.AccessControl.InheritanceFlags]::ObjectInherit
$Propogation = [System.Security.AccessControl.PropagationFlags]::None
$Access = [System.Security.AccessControl.AccessControlType]::Allow
$AccessRule = New-Object System.Security.AccessControl.FileSystemAccessRule("$using:FullUser",$Rights,$Inherit,$Propogation,$Access)
$ACL = Get-Acl $using:ACLPathFull
Start-Sleep 2
$ACL.AddAccessRule($AccessRule)
Start-Sleep 2
Set-Acl $ACLPathFull $ACL
}