First - Rotor copper losses: Measure the resistance of the main rotor field winding, recording the temperature at which you made the measurement, then calculate the I^R losses at the operating temperature (Use the temperature coefficient of resistance of copper) and operating current. This is straightforward as long as you can access the main field windings and you have an accurate microhmmeter. If it has slip-rings - which I assume it will - then it is very easy. You can even measure the I^2R losses if you monitor the main field voltage and current accurately during operation.
Second - do the same for the stator I^2R losses. Measure the stator resistance (and record the temperature), and then use the temperature-corrected resistance and the operating stator current to determine the Stator Copper Losses during operation. Use the rated current if you just want the rated copper losses.
The core losses are the most difficult, and Massimo's experience is obviously the best IF you have the equipment to do this. It involves VERY accurate cooling water flow rate and temperature measurements, which I doubt you will have. You determine the losses by the volume flow rate of water, the specific heat, and the difference in inlet and outlet temperatures.
Realistically - unless the rewinder performed major work on the stator core - the iron losses will be identical to what they were before the rewind. In this respect - the rewinder's core test should be checked for the integrity of the core. In other words - I believe it is highly unlikely that the rewinder affected the core condition during the rewind, BUT if it was damaged when the generator failed - then it is worth at least checking the rewinder's core test results.
Practically - IF the OEM of the generator performed two relatively simple tests on initial manufacture: The Open-Circuit and Short-Circuit Tests. If they did - you will almost certainly have these in your records.
In addition - I suspect you will be able to perform them both with little effort. Run the machine up to speed, with the stator short-circuited, and apply rotor field excitation until rated current is circulating in the stator. Run the machine like this until its temperature rise stabilizes within two degrees C per hour. Record the temperature rise, and the cooling parameters.
The Open-circuit test is similar, with the stator Open-circuited (with voltage measurement capabilities of course), and run at rated voltage for sufficient duration to get the temperature rise to stabilize to within 1 degree C per hour (The temperature rise will be much lower for this test). Record the same parameters. In both cases you can record field current and voltage, to determine the rotor field winding I^2R in each case - but this is not usually required.
If you have accurate temperature and flow-rate measurements on your cooling water - you can determine the losses for each test (what Massimo is referring to). This is ideal - first prize - but I doubt you have such accurate equipment fitted.
All you need to do is compare your open-circuit test and short-circuit test results with those performed by the OEM in the initial factory tests. The SC test determines mainly I^2R losses (and Friction and Windage actually), while the OC test determines main Stator core losses (and of course Friction and Windage), so you will very quickly see if there is a problem with any of the losses.