I am a permanent resident, and received a 1042-S with income code 19. How should I file?

Here's how to report the 1042-S with Income Code 19 (for teaching/research):

To report the Income:

1. Click on Wages & Income 
2. Scroll down to All Income 
3. Scroll down to Less Common Income 
4. Scroll down to Miscellaneous Income, 1099-A, 1099-C 
5. Click start 
6. Scroll down to Other reportable income 
7. Answer yes 
8. Enter description and amount 

To report the US tax paid:

1. With your return open
2. Click on Deductions & Credits
3. Scroll down to Estimates and Other Taxes Paid\
4. Click on Other Income Taxes
5. Scroll down Other Income Taxes
6. Click on Withholding not already entered on a W-2 or 1099

Here's more info on Form 1042-S. 

@shafayat