Do you know what frame size the 3ph motor is? If it's 71 frame for example it could easily be replaced.
no idea of what that is?
As I understand it, the frame size is the area of the motor's flange, where it bolts to a pump for example. I guess the best way to measure this is by measuring the centres between the holes on the motor's flange (is this called pcd?). You also need to measure the diameter of the shaft and it helps to know if it there is a keyway on the shaft.
3phases I think are more efficient, so a 3 phase 0.37kw motor could be 63 frame size, whereas the 1ph equivalent would be 71 frame. I suspect that you could get a 3ph 0.37kw motor in 71 frame though.
Common shaft sizes are 11mm 14mm and 18mm