Processes in Microsoft 365 for setting up Office apps, redeeming product keys, and activating licenses.
Hi,
Welcome to Microsoft Community and thank you for posting the question. As I understand you want to install Office 365 on another computer. Let me help you with the issue.
In order to troubleshoot the issue, refer the link below to know on how to install Office on more than one computer:
http://office.microsoft.com/en-us/support/install-office-on-more-than-one-computer-HA102901468.aspx
Restart the computer once the Office is successfully installed and the other family member can use Office programs, the member can use their own Windows Live ID with the Office 2013 programs in order to save the files to SkyDrive.
I hope the above link helps. If you need further assistance on this particular issue or any other Office related issues let us know and we will be glad to assist you.
Thank you.