You can. You just have to log into their account to download it.
Since you now have to log into an Intuit Account when you first install it, all your downloads and licenses are listed there (even if you bought it from somewhere else) so if you need to install it again or install on another computer, even on the other operating system (Windows, Mac) you can download it again.
How to get started with the Desktop program, install and activate it
https://ttlc.intuit.com/turbotax-support/en-us/help-article/product-delivery/download-software-turbotax-com/L7u9oLEkq_US_en_US?uid=luqgvzrd
To be sure I understand, after insalling the 2024 TTax app, the original purchaser has to sign-in to enter ACTIVATION code on the second computer, then other family members can sign-in to use the app with their own login credentials to complete their returns. Is this a correction assumption?
All returns will be filed under the original login that is associated with the activation code. The software is limited to a max of 5 IRS E-filed returns and 5 computer downloads.