How to pass output from a PowerShell cmdlet to a script?

You should declare your custom function called Prepare-MoveRequest instead of simply making it a script. Then, dot-source the script that declares the function, and then call the function. To accept pipeline input into your function, you need to declare one or more parameters that use the appropriate parameter attributes, such as ValueFromPipeline or ValueFromPipelineByPropertyName. Here is the official MSDN documentation for parameter attributes.

For example, let's say I was developing a custom Stop-Process cmdlet. I want to stop a process based on the ProcessID (or PID) of a Windows process. Here is what the command would look like:

function Stop-CustomProcess {
    # Specify the CmdletBinding() attribute for our
    # custom advanced function.
    [CmdletBinding()]
    # Specify the PARAM block, and declare the parameter
    # that accepts pipeline input
    param (
        [Parameter(ValueFromPipelineByPropertyName = $true)]
        [int] $Id
    )

    # You must specify the PROCESS block, because we want this
    # code to execute FOR EACH process that is piped into the
    # cmdlet. If we do not specify the PROCESS block, then the
    # END block is used by default, which only would run once.
    process {
        Write-Verbose -Message ('Stopping process with PID: {0}' -f $ID);
        # Stop the process here
    }
}

# 1. Launch three (3) instances of notepad
1..3 | % { notepad; };

# 2. Call the Stop-CustomProcess cmdlet, using pipeline input
Get-Process notepad | Stop-CustomProcess -Verbose;

# 3. Do an actual clean-up
Get-Process notepad | Stop-Process;

Now that we've taken a look at an example of building the custom function ... once you've defined your custom function in your script file, dot-source it in your "main" script.

# Import the custom function into the current session
. $PSScriptRoot\Prepare-MoveRequest.ps1
# Call the function
Get-MailUser | Prepare-MoveRequest -RemoteForestDomainController dc.remotedomain.com $Remote -LocalForestDomainController dc.localdomain.com -UseLocalObject -OverwriteLocalObject -Verbose;
# Note: Since you've defined a parameter named `-WindowsEmailAddress` that uses the `ValueFromPipelineByPropertyName` attribute, the value of each object will be bound to the parameter, as it passes through the `PROCESS` block.

EDIT: I would like to point out that your edit to your post does not properly handle parameter binding in PowerShell. It may achieve the desired results, but it does not teach the correct method of binding parameters in PowerShell. You don't have to use the ForEach-Object to achieve your desired results. Read through my post, and I believe you will increase your understanding of parameter binding.