Rewrote the answer:
Assuming that you really want to use the thevenin equivalent of the combination generator + transmission line, the T.E. should be derived properly. You should find the output voltage when the load is disconnected (=Eo) and the output current when the load is 0 Ohms. Let that be Io.
Then your equivalent has the source voltage Eo and serial impedance Eo/Io
Calculating Eo and Io should from the very beginning take into the account that it takes some time the signal to travel through the line. It causes phase difference. The whole calculation should be done in phasor domain by using complex numbers. The result would contain, how long is the delay on the line, what is the frequency and the line charasteristic impedance also should exist in the right formula. The line impedance is not a resistance . It's needed when calculating the voltage and current components of a propagating wave. At both ends also should the reflected wave exist in the calculation.
Maybe you have thought that the line can be considered as a serial element with the load. Unfortunately it's a two port (= quad pole). That, how the signal source sees the load through a two port,can't be calculated by adding two impedances - not even in complex phasor domain.