Copying data from one SQLite database to another
You'll have to attach Database X with Database Y using the ATTACH command, then run the appropriate Insert Into commands for the tables you want to transfer.
INSERT INTO X.TABLE SELECT * FROM Y.TABLE;
Or, if the columns are not matched up in order:
INSERT INTO X.TABLE(fieldname1, fieldname2) SELECT fieldname1, fieldname2 FROM Y.TABLE;
Easiest and correct way on a single line:
sqlite3 old.db ".dump mytable" | sqlite3 new.db
The primary key and the columns types will be kept.