If he will need to use his second US passport for travel while the visa application is pending, he can keep it. In this case, he can explain in a covering letter that he has not included it with his application due to the need to travel while the application is processing, and include a photocopy of the details page.
Otherwise, if he's not expecting to use it and is okay to be without it for several months, include it in the application and clearly denote which passport is his primary one. All passports in his possession (current and expired) should be included. If unable to include one (for example, it was lost/stolen), provide as much information about it as possible in a covering letter.
