A function that checks for the new Exchange Online Management Shell and will use it if it's available. Otherwise, it falls back to the old connector, but with a warning.

FN_Connect-EOCustom.ps1

function Connect-EOCustom {
    if(Get-Command Connect-ExchangeOnline -ErrorAction SilentlyContinue) {
        #The new module is installed
        Write-Host "You have the modern management shell installed, it will be used to connect to EO!" -ForegroundColor Green;
        Import-Module ExchangeOnlineManagement;
        Connect-ExchangeOnline;
    } else {
        #the new module is not installed
        Write-Host "NOTICE: You are not using the modern management shell. The old shell will soon be deprecated, but the script will continue for now." -ForegroundColor Yellow;
        Write-Host "It is strongly recommended that you install the new shell using Install-Module -Name ExchangeOnlineManagement" -ForegroundColor Yellow;
        Pause;
        $UserCredential = Get-Credential;
        try {
            $Session = New-PSSession -ConfigurationName Microsoft.Exchange -ConnectionUri https://outlook.office365.com/powershell-liveid/ -Credential $UserCredential -Authentication Basic -AllowRedirection
            Import-PSSession $Session;
        } catch {
            Write-Host "Couldn't connect to Exchange Online." -ForegroundColor red;
            Pause;
            exit;
        }
        
    }
}