something like:
CREATE TRIGGER
schema1.triggername
AFTER INSERT ON schema2.table
FOR EACH ROW
BEGIN
;
END;
ERROR 1435 (HY000): Trigger in wrong schema
something like:
CREATE TRIGGER
schema1.triggername
AFTER INSERT ON schema2.table
FOR EACH ROW
BEGIN
;
END;
ERROR 1435 (HY000): Trigger in wrong schema
The trigger needs to be in the same schema as the table you are inserting to, but it can access tables in other schemas.
Using your example:
CREATE TRIGGER schema2.triggername
AFTER INSERT ON schema2.the_table
FOR EACH ROW
INSERT INTO schema1.the_table values (...);