You can both use the 1098-T to make your entries. If you claim the tuition credit, you do need to report that you got one (the TurboTax interview will handle this) Your student should use the 1098-T because it makes entering scholarship income go smoother and puts the income in the right place on the tax forms, line 8r of Schedule 1 (this is a new location starting in 2022).
TurboTax can theoretically handle all that when you follow the interview carefully. But, it goes smoother if you use a work around in TurboTax (TT). Here's how I would do it. Enter the 1098-T, on your return, but only enter $4000 in box 1. No other numbers. You only enter the 1098-T to get TurboTax to check the proper box on form 8863. Lying to TurboTax to get it to do what you want does not constitute lying to the IRS. The 1098-T that you enter in TT is not sent to the IRS.
Enter the 1098-T, exactly as received, on the student's return. Enter book and computer expenses separately. In his interview, you should eventually reach a screen called "Amount used to calculate education credit" (or similar wording). Be sure the amount in that box is $4000. You must complete the “education information” subsection to get that screen, This will put all his excess scholarship as income on his return (line 8r of Schedule 1).
Be advised some people are saying they're not getting the "Amount used to claim the tuition credit" (or “Education Expenses used for a Tax Credit”) screen on the dependent’s interview. Check the student information work sheet (part VI, line 17) to verify it was entered. If not, the alternate workaround is to enter $4000 less than the actual box 1 amount, when you enter the 1098-T.
There's yet another (and simplest) work around. Manually calculate the taxable amount of scholarship and enter the 1098-T, on his return, with 0 in box 1 and the taxable amount ($15,900* in your case) in box 5. In that case the amount in the "Amount used to claim the tuition credit" box is 0 (if it comes up).
Before doing that, it may be helpful to first delete the previously entered 1098-T and start over, so that there's not conflicting data still hanging around.
*24,000 - 10,600 -1500 +4000 = 15,900
