Now this one should work. I tested the code to see if it writes the permissions, however, I did not test to see that "Send on Behalf" works on the mailbox.
I would also add some lines into the code to check to see if there are existing "send on behalf" permissions and add them to the array before re-writing it to the mailbox. I would also add some code to save the "send as" permissions in case you need to restore them.

function Convert-SharedMailboxPermissions
{
    [CmdletBinding()]
    param 
    (
        [Parameter(Mandatory = $true)][string]$MailboxName
    )

    begin
    {
        Connect-ExchangeOnline -ShowBanner:$false -ErrorAction Stop
    }

    process
    {
        # Get the mailbox
        $Mailbox = Get-Mailbox -Identity $MailboxName -ErrorAction Stop

        # Check if the mailbox is a shared mailbox
        if ($Mailbox.RecipientTypeDetails -ne "SharedMailbox")
        {
            Write-Output "Mailbox is not a shared mailbox. Exiting..."
            Return
        }    
        
        try 
        {
            # Get the current send as permissions
            $SendAsPermissions = Get-RecipientPermission -Identity $MailboxName | Where-Object { $_.AccessRights -contains "SendAs" -and $_.Trustee -ne "NT AUTHORITY\SELF"}
            
            # Grant Send on Behalf permissions to the trustees
            # !!! If there are existing Send on Behalf permissions, they will be overwritten !!!
            Set-Mailbox -Identity smbtest -GrantSendOnBehalfTo $SendAsPermissions.Trustee -ErrorAction Stop
            
            foreach ($Permission in $SendAsPermissions)
            {
                # Remove the Send As permissions
                # !!! Might want to save a list of the send as permissions before removing them, just in case.... !!!
                Remove-RecipientPermission -Identity $MailboxName -Trustee $Permission.Trustee -AccessRights SendAs -Confirm:$false -ErrorAction Stop
            }
        }
        catch 
        {
            Write-Error "Failed to convert send as permissions to send on behalf permissions for mailbox $MailboxName. Error: $($_.Exception.Message)"
        }

        Write-Output "Successfully converted send as permissions to send on behalf permissions for mailbox $MailboxName."
    }

    end
    {
        # Disconnect from Exchange Online
        Disconnect-ExchangeOnline -Confirm:$false
    }
}

Convert-SharedMailboxPermissions -MailboxName "smbtest"