Should be possible using two statements within one transaction, an insert and a delete:
BEGIN TRANSACTION;
INSERT INTO Table2 (<columns>)
SELECT <columns>
FROM Table1
WHERE <condition>;
DELETE FROM Table1
WHERE <condition>;
COMMIT;
This is the simplest form. If you have to worry about new matching records being inserted into table1 between the two statements, you can add an and exists <in table2>
.