I am an Assistant AEO for my squadron. Our Primary AEO is presently deployed and our Activity Report is due soon, can I submit the Activity Report for him or is this my Commander's responsibility?

You should coordinate with your Unit Commander. The chances are that they will want you to enter the data, so that they can review and approve it afterwards. However, the Unit Commander may opt to do it themselves or with you, depending on how long you have been an Assistant AEO.