An Italian company has a postdated English check in hand can he cash in before time?

A cheque can be cashed only on or after the cheque date.

Ex: Let us say you issue a cheque to Mr. xyz today (June 2nd 2009) and mark the cheque date as July 1st 2009 (A post dated cheque)

Mr. XYZ can deposit this cheque on or after July 1st 2009. If he tries to deposit before that date, the bank would reject it. A cheque is a valid and legal instrument for money transactions only after the cheque date.