I often sync using my phone and activities transfer across without issue.
The connection between the websites is what matters. Make sure that they are connected using a computer.
In Strava, check you have a connection under Settings. You should see a number of Social Connections on the right hand side of the page.
You can also check on Garmin Connect by going to Head and Shoulders > Account Information. If they are linked, you will see Strava listed under Applications with Read Permission.
If both of those are good, you should be good to go.
In both cases, the Strava and Garmin Connect mobile apps are picking up what is set on the websites. I always find it better to make changes on the websites.