Modifying a stored procedure saves locally, how to save to the database? (4265179)

How do I save it so that the changes are saved back to the DB and not my desktop or local pc?

Currently, I right click on the Procedure that I'd like to modify, select Alter Procedure and make the changes.

To save altered procedure code, the Execute/compile icon needs be used. Click the first icon that is a green triangle, Execute SQL.

Or from the main menu select Editor | Execute SQL

Or use F5 key.

To see changes:
Right click on database object |Send To |Object Details | Script tab