check_folder_permissions_AD.ps1

$Folder = "S:\path\to\folder"
$User = "Jane Doe"

$userPermissions = @()
$userPermissions += (Get-ADPrincipalGroupMembership $User).name

$folderPermissions = @()
$folderPermissions += (((Get-Acl $Folder).Access).IdentityReference).Value

$match = 0

foreach($i in $folderPermissions){
    foreach($j in $userPermissions){
        if($i.contains($j)){
            $match = 1
            Write-Output "$User is a member of the security group $j which grants the user access to $Folder"
        }
    }
}

if($match -eq 0){
    Write-Output "$User does not have access to $Folder"
}