How can I verify the value of a parameter being passed into a mocked function using Pester

I have a function written in PowerShell and I am trying to test that function using Pester v-5. I have included the function under test and the Pester test case in the code samples below.

I am trying to verify that the parameter $FileName being passed into the mocked function Save-Report is correct. How can I do that?

Notes:

• I realise the value of that $Filename parameter is being set to a test value when I mock the function Add-StringToFileName and return a test value. But I still want to test that the value makes it down to the end and remains unchanged.
• This is definitely something that I would like to do in future tests so I want to understand how it can be done.

Function under test

Function Invoke-ReportDownloader
{
    [CmdletBinding()]
    Param
    (
        # The command object used to connect to the database
        [Parameter(Mandatory)]
        [System.Data.Odbc.OdbcCommand]$Command,

        # An XML element containing the report item to be retrieved
        [Parameter(Mandatory)]
        [System.Xml.XmlElement]$ReportItem,

        # Hashtable containing the configuration parameters
        [Parameter(Mandatory)]
        [hashtable]$ConfigParams,

        # The SEMO participant that the report is being downloaded for
        [Parameter(Mandatory)]
        [System.Data.DataRow]$Participant
    )

    # If report is not supported jump to next report
    $ReportName = $ReportItem.ReportName
    if (-not (Test-ReportSupported $Command $ReportName)) {
        $Logger.Warning("Report: $($ReportName) is not currently supported")
        return
    }

    # (Kanban-7940) If there is no date included in the specified file name in
    # the report item then we append the associated date to the filename. This
    # is to avoid multiple reports of the same type overwriting each other.
    $Filename = $ReportItem.FileName
    if (-not (Test-TimestampIncluded -Filename $Filename)) {
        $FileName = Add-StringToFileName -Path $Filename -SubString $ReportItem.Date
    }

    # If report already exists in database jump to next report
    if (Test-MarketReportInDatabase $Command $ReportItem) {
        return
    }

    Get-Report $ConfigParams $Participant $ReportItem

    # If the response contains failure information throw an exception
    $ReportSuccessParams = @{
        ResponsePath = $ConfigParams.BmResponsePath
        BaseName = $ConfigParams.ReportFilter
    }
    if (-not (Test-SuccessfulResponse @ReportSuccessParams)) {
        throw "Unsuccessful response from BM"
    }

    $SaveReportParams = @{
        RawPath = $ConfigParams.RawPath
        XmlResponsePath = $ConfigParams.XmlResponsePath
        Filename = $FileName
    }
    Save-Report @SaveReportParams
}

Unit tests

Describe 'Invoke-ReportDownloader' {
    BeforeAll {
        # Set up test $Cmd object
        # Set up test $Logger object
        # Set up test $ReportItem object
        # Set up test $ConfigParams object
    }

    Context "No timestamp included in the filename" {

        BeforeAll {
            Mock Test-ReportSupported { return $true }
            Mock Test-MarketReportInDatabase { return $false }
            Mock Get-Report
            Mock Test-SuccessfulResponse { return $true }
            Mock Save-Report
        }

        BeforeEach {
            $Script:ReportDownloaderParams = @{
                Command = $Script:Cmd
                ReportItem = $ReportItem
                ConfigParams = $Script:ConfigParams
                Participant = $Script:Participant
            }
        }

        It "Should save the report with the timestamp included in the filename" {
            $TestFileName = "test_string_20210101"
            Mock Add-StringToFileName { return $TestFileName }
            Invoke-ReportDownloader @Script:ReportDownloaderParams
            Should -InvokeVerifiable Save-Report
            # I want to verify here that the parameter $FileName being passed into the mocked function Save-Report is correct.
        }
    }
}

You can confirm a mock was called with specific parameters as follows:

Should -Invoke -CommandName Save-Report -Times 1 -ParameterFilter { $Filename -eq "test_string_20210101" }

See https://pester-docs.netlify.app/docs/usage/mocking#example for more details.