You are asking two questions.
How can the electron jump instantaneously.
How can the other atoms know instantaneously that this atom already absorbed the photon and there is nothing to absorb for the others.
The wavefunction is the probability distribution of the particle's position. For the photon, the wavefunction will give you a description of the probabilities of the photon's trajectory. For the electron in the absorbing atom, the wavefunction will give you a probability description of what energy level the electron is at as per QM.
Now you are saying that the electron in the absorbing atom will jump up an energy level when absorbing the photon and then it will jump back down when emitting a photon. But this is not right. As per QM, there is no quantum leap. The wavefunction describes the position of the electron at certain energy levels, and the probability that the electron is at a certain energy level is higher then the other ones. Classically we would say that the electron is at that orbit. But in QM, the electron is just at that energy level with a high probability and is at other energy levels with a lower probability at the same time.
At the same time is important. You could find the electron at other energy levels too, just with lesser probability. When the electron absorbs the photon, it does not jump. It does not travel to a higher energy level classically. What happens, is that the wavefunction changes. It will describe the electron's probability to find it at a higher energy level with higher probability. And at the original lower level with lesser probability. As per QM, the electron moved to a higher energy level. But the electron did not jump classically. The electron can be found at the same time at both energy levels, it is just the probability that changed, the higher energy level has now higher probability.
Your confusion is about how the electron jumps instantaneously. It does not. It is the probability (of finding the electron at a certain energy level as per QM), and the wavefunction that changes instantaneously as per QM.
It is not only the electron and the photon that have wavefunction. All the atoms have one.
The wavefunction is just information. It does not collapse classically. It changes. It is a probability description. The positions of the particles in this case are described and probabilities are assigned to them. That can change instantaneously.
When the atom absorbs the photon, the photon transforms into energy, and the photon does not exist anymore. It is added to the energy level of the electron.
This interaction is not instantaneous. It needs the average time of EM interactions.
You are asking then how is it possible that other atoms know they do not need to absorb the photon. It is because the photon is the excitation of the EM field. The EM field exists everywhere in space. The atoms nuclei (and their constituents) and the electrons are excitation of those fields. Those fields exist everywhere in space. The two kinds of fields can interact (the EM for the photon and the electron and the other fields of the nuclei's constituents).
When the two fields interact, and the atoms' energy level's gap is compatible with the energy level of the photon, it will be absorbed. The photon then does not exist anymore, it transformed into the energy level of the electron.
Though the photon travels as a wave, it's probability distribution will describe it's position in space for different positions at the same time. At the same time is important. When (at a point in time) the wave reaches the screen, there will be a position of the photon that has the highest probability at that time. Other positions of the photon at the same time have lesser probability around that area. The atoms around that position (the position of the photon with the highest probability at that time) have a wavefunction, that describe their positions and energy levels gaps. The atom that has the matching energy level gap that matches the photon's energy level will absorb it with the highest probability.
The interaction between the atom and the photon is not instantaneous. It needs the average time for EM interactions. But the change in the wavefunction can be instantaneous, and the probability description of the absorbing electron's energy levels has changed. The photon does not exist anymore. It transformed into the energy level of the electron.
The other atoms cannot absorb the photon for two reasons.
The photon's position has a probability description (wavefunction) and at the point in time when the photon hits the screen, there is a position with the highest probability. Only atoms around that area can absorb the photon. And only atoms around that area with matching energy gap can absorb the photon.
The wavefunction can change instantaneously. The photon after the interaction does not exist anymore. It transformed into the energy level of the electron.
No particle or object can travel faster then light as per SR. But the wavefunction is just information, and it describes the particles' characteristics' probabilities. Those probabilities can change instantaneously (because the wave function is not a physical object). But even if that changes instantaneously, no particle or object of information travels faster then light.