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You want immediately to use the principle of relativity. But historically there was still no theory of relativity. So, we have an absolute ether. How do you want to proceed then?
Think about it that the vector of velocity and the vector of field strength are physically different. You can not somehow unite them, e.g. by an addition.
Just show mathematically how it works. How can two second-order factors, length contraction and time dilation (~ [1 - v2/c2]1/2, for v << c => ~ 1 - [v/c]2/2), completely compensate one first-order factor, the inclination of the field strength (for v << c, ~ v/c) ?
... the actual angles
And you know that the information about the current position of the emitter can not be transmitted instantly over long distances? The maximum transmission speed is known to be the speed of light.
If the wave reaches the receiver,My opinion: From the point of view of the recipient, this is inclined and point to its place of origin.Your (and Lorentz&Einstein) opinion: From the point of view of the recipient, this is directly and point to actual position of the emitter.
Meanwhile I thought about what the experiment might look like (see figure below). The receiver consists of two dipole antennas, these are perpendicular to each other and at an angle of 45 ° to the emitter. If the wave front passes the receiver flat, the signals in the antennas balance out. Then SR or LET is valid. And on the contrary, both are invalid.