Particle colour based on emitters image texture?

Support Particles and Physics Simulations
1

I have 2 objects in my scene. One is an object which has a rainbow image texture surrounding it. The second is a sphere.

I’m applying a particle emitter to the rainbow object and making the particles themselves be the sphere object.

What i want is for the particles to have the same colour as the object depending on where it was emitted from.

Is this possible?

2

Yes.
In material of particle object, you have to set-up the texture and enable From Dupli option at the bottom of Texture Coordinates node.