In the scenario you described, where two photons A and B are entangled, and the position of photon A is measured just before photon B encounters a double slit, the behavior of photon B depends on the specific nature of the entanglement and the measurement performed on photon A.
Entanglement is a fundamental concept in quantum mechanics, where the properties of two or more particles become correlated in such a way that the state of one particle cannot be described independently of the others. When two photons are entangled, measuring a property of one photon can instantaneously affect the state of the other, regardless of the distance between them.
Now, when the position of photon A is measured just before photon B encounters a double slit, it collapses the wavefunction of photon A into a definite position eigenstate. As a result, the entanglement between the two photons causes the state of photon B to also collapse into a correlated state.
The exact behavior of photon B, whether it behaves as a wave or a particle, depends on the details of the entanglement and the specific measurement performed on photon A. If the entanglement between A and B is such that the wave nature of photon A is strongly correlated with the wave nature of photon B, then even after the measurement of photon A's position, photon B is more likely to exhibit wave-like behavior as it passes through the double slit.
However, if the entanglement and measurement scheme are such that the wave nature of photon A is not strongly correlated with the wave nature of photon B, or if the measurement of A collapses its wavefunction into a state that is incompatible with wave-like behavior for B, then photon B may behave more like a particle as it passes through the double slit.
In summary, the behavior of photon B, whether wave-like or particle-like, after the position measurement of photon A depends on the specific details of the entanglement and the measurement scheme used. The entanglement and measurement can influence the correlation between the particles and determine the subsequent behavior of photon B.