Have you tried using DISTINCT:

SELECT DISTINCT FA960.*, UMCONVPZ.UMFR, UMCONVPZ.UMCONF AS Piezas, UMCONVPL.UMCONF AS PL, UMCONVCJ.UMCONF AS Cajas FROM FA960 FA960 JOIN UMCONV UMCONVPZ ON UMCONVPZ.UMRESR = FA960.RECURV AND UMCONVPZ.UMFR = FA960.RMUMSR AND UMCONVPZ.UMTO = 'PZ' JOIN UMCONV UMCONVPL ON UMCONVPL.UMRESR = FA960.RECURV AND UMCONVPL.UMTO = 'PL' JOIN UMCONV UMCONVCJ ON UMCONVCJ.UMRESR = FA960.RECURV AND UMCONVCJ.UMTO = 'CJ' 

It's tough to say without knowing more about the data.