Teach SHAPES.
Every chord inversion is the same shape!! 1-3-5 is root, right?
Well, 1st inversion is 1-2-5; 2nd inversion is 1-3-5. (the numbers being the fingers)
In C: R= C-E-G (1-3-5), 1=E-G-C (1-2-5), 2=G-C-E (1-3-5)
One thing I notice newbies tend to do is to play chord inversions (even if the notes are right) with the wrong fingers. They play whatever feels good to them. Which is ok short term, but sets them up for having a tough time with those exact same inversions in different keys.
Learn the shapes first and your fingers will "remember" the shapes in any key. Of course, you have to play the right notes too.
In the key of G:
R=G-B-D (1-3-5), 1=B-D-G (1-2-5), 2=D-G-B (1-3-5)
In the key of D:
R=D-F#-A (1-3-5), 1=F#-A-D (1-2-5), 2=A-D-F# (1-3-5)
In the key of E:
R=E-G#-B (1-3-5), 1=G#-B-E (1-2-5), 2=B-E-G# (1-3-5)
And so on. A good exercise is to pick a key and just do the inversions all the way up the keyboard. Get the shapes under your finger.
Another TIP is to coach them to play the right hand as "smoothly" as possible. How do you get a "smooth" keyboard sound. DON'T jump around on your chords. Learn the inversions and then pick a pattern that is not choppy. Find the nearest inversion for the next chord coming up and move as few fingers as possible.
For example:
In the key of G:
Say we're starting on G (1st inversion) = B-D-G (1-2-5) and the next chord is C.
We'll want to find the nearest inversion of C and try and move to it smoothly. I'd move to C in Root position C-E-G (1-3-5) moving the B to the C (1 to 1) and the D to the E (2 to 3). To simplify that even more and to make it even more smooth. Keep the D in both chords (B moves to C and D stays the same. Only the thumb moves. So in essence you move from a G (1st inversion) to a C2 (Root and omitting the third).
Good luck!