Yes you can - since you already created the schema from the TYPE - the TYPE should already exist and is technically shared. The TYPE folder contains the shared type.
In the new Schema - you would just simply ASSIGN that type to the Schema and connect your mappings.
Let me know if this answers your question.
That is because it exists already as a Shared TYPE - in your Types folder. If a Schema is using a TYPE that is not local - such as the default Composite type - then it cannot be shared if it is already shared. Look at your Types folder and note that you have a Type named Facility. This Type - is your already shared Type.