Unlike other links, which can be managed from the links tab on a quotation. job/sales order. etc., this needs to be set using the Project field.
1. To assign a quotation, job/sales order to a project. this field needs to be visible
2. If it is not, click on "Screen Options"
3. Click on the switch to make the "Project" field visible
4. To assign it to the project, click here
5. Find and select the desired project
6. If you have the project open in another screen when making this change, refresh that screen (F5) so it has the latest data.