Hi Kjell

Electrically it doesn't matter, because a J-Pole consists of a 1/2
wave antenna sitting on top of a 1/4 wave matching section.
Mechanically, one leg of the matching section is integral with the
antenna to save the cost of a fitting.

However, in real life, connecting the center conductor to the stub
lowers the receive noise level of the antenna slightly without
affecting performance.
Albeit, placing three 1/16th wave wires extending from the top cap,
sorta like a capacity hat, will do the same thing.

TTUL
Gary