Robin, thank you
The oxycon is new, so all filters are fresh and clean.
I did a test last night - lighted the torch with oxy valve open and it worked like a dream - no oxy flow problem at all. May be it is not the safest way, but I failed to resist trying the torch that was waiting for almost half a year. And today I spent about 5 hours - no single problem until I close the output while the oxycon is working. It seems this is all about it's control unit.
I am thinking about adding a 3-direction fitting into the oxy line with the switch to "trigger" output to the torch and to the side (I can add it within my reach but far enough from the torch and lighter) to close the line to the torch when I need without interrupting the flow from the oxycon.