Your ability to do this is limited by the amount of time you would like to invest and the cooperative spirit of server administrators.
Frankly, you cannot trust any email header that appears in the message headers regarding the delivery route that is beyond a server that you control. For most people, this means that you can only trust that your server received it from the server that it identifies by address and name.
To determine whether or not this is the actual source, you would have to contact the owner of that system that most immediately delivered the mail to your server with the relevant time and information about that message from your mail delivery logs. Using that information, if he is so willing, he can extract data from his server log to tell you which server gave it to him. You probably begin to see the issue here.
If he is unwilling, that is no indication that his server was the origin of the spam. However, if he is unwilling, your trail also immediately turns cold.
Hope this helps!