At work we auto forward our inboxes so that anyone on the team can answer them if we're not there. If I forward someone else's inboxed message, can the original recipient (my coworker) tell that I did it?
Gmail forwarded messages contain information that shows the path a message took.
You can see this information by reviewing the message header of one of the forwarded messages using the "Show Original" option.
Therefore your new forward would add that information to the header. In order for this to be exposed to the original recipient, they would need access to the forwarded message, or the recipient you forward it to would need to reply to the message.