para simular FULL JOIN
en mysql, necesitas UNION
el resultado de Right Join y Left Join de ambas tablas
SELECT Persons.Name, Persons.P_Id, Invoice.Id
FROM Persons
LEFT JOIN Invoice
ON Persons.P_Id=Invoice.P_Id
UNION
SELECT Persons.Name, Persons.P_Id, Invoice.Id
FROM Invoice
LEFT JOIN Persons
ON Persons.P_Id=Invoice.P_Id