Check output voltage - it will be AC, remember, by measuring voltage across any two of the 3 white wires emerging from the cases. This is 3 phase AC, so you want to check every combination of two wires (1-2, 1-3, 2-3). If you notice any defect in the 3 connector plug, that looks like it may have partially melted, or gotten really hot - you should remove the plug completely, just cut the wires off both ends. The remaining wires can be soldered together. Being AC, it does not matter which stator wire you solder to which R/R wire - just be sure to do a good job, and insulate them well.. From each other, as well as ground!
Lots of these plugs fail due to corrosion causing increased resistance in the plug. This causes excess heat at the point of resistance, and can lead to a hot, melted, or even burning connector. Mine smoked, and has been soldered for the last 20 years. I had to replace a couple R/R units over the time, just a bit of soldering and heat shrink tubing, and it's as good as new...
Output voltages across any two of the stator wires should be about 50 (there is a wide variance here that still is considered OK), but should be within a few volts of each other. You can also measure resistance of the stator coils, and measure for shorted phases of the stator. I don't remember what the resistance of the stator coils is supposed to be, something like .5 ohms seems right. If you have zero ohms between any white wire and ground, the stator is shorted to ground and is kaput. Others have posted info on how to test these functions.