"Note: If you have not published your layer using the steps in the previous tutorial and you are connected to ArcGIS Online, you can use a shared editable feature layer to follow the rest of this tutorial. To use the shared layer when you follow the steps below, search all of ArcGIS Online for damage assessment demonstration and add the layer authored by esri_collector."
The layer has these capabilities: Query,Create,Update,Delete,Uploads,Editing
This layer is coming from an ArcGIS Server and does not support sync so you will not be able to take this service offline. You will need to create a copy of the service in AGOL to have it offline capable. To create a copy of the service you can follow the Publish an Empty Feature Layer steps in the ArcGIS Online help doc here. Then you can enable sync by following these steps outline in our doc
Once you have your feature service ready you can create a web map with it and once it is saved you will see it in the Collector app when you refresh the map gallery.
To Collect and Edit features these two links in our doc should help you out. Collect Edit