A suggestion would be to form a list of behaviors that you want to change. Review that list and break it down into at least two maybe three categories: Must Change, Want to change, Wish would change. Probably want to tackle one or two of the Must Change items first.

Since your son is 11 and as you said, it is not his fault that he has developed habits based on living in a different household... you and his dad could sit down together during a calm moment and have a discussion about what behaviors MUST be changed. I would not dump the entire list on him - you want to encourage him without making him feel bad about himself. Try really hard to clearly identify the behavior you need to have him change but that you love him just as he is.

You could work with him to come up with how he might change. and then support him - and keep tabs to ensure it is working.

For example, perhaps he is in the habit of staying up until 11pm playing video or watching TV. HW isn't getting done and he is a bear to get up for school. Getting to bed earlier - even by an hour - could be a goal. Perhaps a complimentary goal would be that all HW must be done before screen time.

Don't expect him to like it - he will probably really hate the earlier bedtime. It is so funny to me that as kids .. we wanted to stay up really late and fought bedtime every single school night .. but now that I'm an adult .. I can't get in bed as early as I would prefer ! lol

Hope this helps