Tip for next time - when having to lift a toilet, and you have at least a fingertip gap between the tank and the wall, you can do a vertical lift in the following manner:

1. Take the tank lid off, disconnect the water feed.
2. Drain the water from both the tank and the bowl. Bowl can be done by taking a large sponge or plunger and just ramming those down to push the water through the S-bend.
3. Stick one hand down into the bowl’s drain hole, curl fingers up into that S-bend to hold it like a pail handle. Use a small face towel (don’t know the English term) if you need padding.
4. Hold the back side of the tank with your other hand to stabilize the entire toilet.
5. Lift with the hand that is in the drain hole.

The weight of the tank should balance out the weight of the front part of the bowl, giving you a reasonably balanced object, albeit not a light one. By lifting from the drain hole, you are putting the lifting motion close to the centre of gravity, making it a lot less awkward. If that is still too much weight, unhook the tank from the bowl and move separately, just be aware this will make the bowl quite front-heavy, you will need to switch hands and stabilize from the front of the bowl.

But still lift from the drain hole, it will still be easier than most any other method.

Source: not a plumber, but have done my fair share of toilet swaps in my time. Blue-collar jack-of-all-trades father who worked as head of maintenance at a large hotel showed me that trick.