According to the TurboTax license agreement you can install the software on any computer you own. So since you don't own your son's computer, you should not give him your software. The following is the part of the license agreement regarding the software.
Supplemental License Grant and Restrictions. In addition to the General License Grant you may: (I) install and use a copy of the Software on one or more computers owned by you (at home or at work); (ii) use the Software only to prepare, print and/or electronically file federal 2016 tax year returns and related state tax returns as described below; (iii) make one backup copy of the Software for personal use as permitted under this license grant; and (iv) any software that is delivered by electronic transmission (regardless of whether a replacement copy is ordered) shall be deemed delivered on the date that Intuit makes such program available for download.
