Collision of falling and thrown upward balls

Hi,

I am wondering if total momentum of the system is conserved in this case. Our system is consisted of two balls: one is falling vertically down to ground, another is thrown vertically up, so they collide in air. Is total momentum of the two balls conserved after the collision?

Now I know that if no external force is applied in the direction of momentum, is is conserved. But here there is gravitational force in the direction of the initial momentum. So I am not sure if total momentum before and after collision is conserved. Any help will be very appreciated.

Sincerely,
Nikola