Three months after investing in four companies with manufacturing plants in Puerto Rico, President Donald Trump’s pick for Health and Human Services secretary introduced legislation that would directly benefit those companies.

The proposed House legislation by Rep. Tom Price—which would have made permanent an expiring tax deduction for Puerto Rican facilities—didn’t pass, and the tax deduction expired Jan. 1. And Mr. Price, a Georgia Republican, testified last week that his broker made all of his stock investment decisions...