Short answer: Not exactly, but can get close.
This is a very frequently asked question, and is usually answered as:
- Solo / emphasize the neck pickup
- Get a stronger neck pickup
- Run pickups in series
- Boost your low-mids
In my experience, those approaches can make a J bass occupy the same sonic spectrum like a P bass. But it won’t sound the same.
Compared to a P pickup, Jazz pickups are thin pickups with a different placement, which means that they capture a narrower & different sonic spectrum and have different natural overtones. That means a different timbre / tone.
To a certain extent, neck difference affects the output as well.
But if that’s close enough for you, fine! Many players get by just fine that way.
Here is a much more detailed explanation.