How does it not function correctly?
The newest trigger bars all have the curved portion where the trigger spring attaches. The one that comes with the G19 of the serial number prefix you listed is Glock manufacturer part number 2303, it has a grooved/serrated trigger pad. The trigger bar made for the Gen3 G17, manufacturer part number 357, will also work in that gun, it has a smooth trigger face.
When replacing a trigger bar, connector, or firing pin, you should use an orange Armorer's slide cover plate to check the engagement between the firing pin lug and trigger bar cruciform. With the slide forward and the trigger fully forward, at least 2/3 of the trigger bar cruciform sear tab should be covered by the firing pin lug. If it's any less than that, it's advised to swap parts with replacement ones until that level of engagement is achieved.
Here are some detail strip resources if you need them:
Correct slide stop spring position: http://glocktalk.com/forums/showpost...29&postcount=3
On the following page are some Glock Armorer's Manuals, just scroll down to the "G" section. I learned from the Update Manual and 2009 Manual. The 2009 Manual has a few pages missing, but that info can be found in the Update Manual as well.
Here's an easy way to disassemble and reassemble the firing pin assembly: