Fthirty have option to send this invoice to client which is related. Also the PDF invoice will be attached to the email. If you want to do not attach the PDF invoice simple uncheck the checkbox Attach Invoice PDF
After sending the invoice to the client if you want to send again the invoice there will be another email content. Becuase the initial invoice is already sent. Now the client maybe want the invoice again and in all cases this content will be different.
Go to Setup-> Email Templates -> Invoice Already Send to Client to edit the email content.
By default all contacts with permission invoice will be selected you can adjust to your needs.