When you say it fires up for 15 seconds - when it quits can be it be re-started for another 15 seconds again and again, or does it just die and will not allow you to start it for hours later? Was it doing the exact same thing before you rebuilt the carbs and replaced the fuel pump?
What happens when it's running if you use the warm up lever (very slightly) to raise the RPM - does it still stall? What happens if you push the key switch in (to operate the choke/electric primer) ?
Try manually pumping the primer bulb after starting the engine to see if it will keep running. If possible, take the cover off the air intake and verify that the carbs are not flooding (or find another way to inspect it while the engine is running) - such a condition would likely flood the engine out at idle after a short period of time and may not be noticeable with the cover on.
Check for any loose wires that might be grounding out or causing an open circuit in the ignition system. By running it with the cover off you may see a little puff of smoke here and there to indicate such a problem.
If when the engine quits it stays dead for awhile, verify how the spark is working after allow it to rest, then start it up and cause the condition, then check the spark on each cylinder again. Sometimes dead ignition components can work again and again just for a matter of seconds until failure.
Another possibility is the butterflies on the carbs (or one of them) is out of sync with the rest of the linkage and is starting completely closed. That would cause a condition where the engine would be choking out, so it could fire for a second but after slight warm up it would be running too rich and would stall.
Jon