I assume that this is not a straight database port, like unattaching the database and reattaching it on the new server/location.  If you were moving settings from one to another, you just have to keep the primary/foreign keys in sync.  So, if it's a new database, and your PKs aren't that high, yet, you would just turn on IDENTITY INSERT when you copy the records from one database to another so they stay in sync.  Otherwise, you'll need to create a dictionary of old/new entries to allow you to assign the proper PK to the child record when you create it. 

When you copy records, you don't have to worry about the project_computer_tie table because it is used to link a project to a development computer.  The so, you'll need to create the project header record, the project items records and then the project item exceptions records.