Best regards to everybody for discussion. I clarify at last the situation for myself. B767 FCTM states:
"...during the last hour of ETOPS cruise, the FAA currently requires that a fuel crossfeed valve check be performed on airplanes with a single crossfeed valve. This verifies that the crossfeed valve is operating so that on the subsequent flight, if an engine fails, fuel feed is available from both main tanks through the crossfeed valve."
Thanks...