I have a brand new wheelchair motor that a friend gave me.
It's a 24V motor.
I don't have any information about the electrical connections to the motor.
Is there someone who by chance knows what the outputs are?
My goal is to control the motor with Arduino and H-bridge.
You will need a suitable brushless DC motor driver, rated at more than 250W, NOT an "H-bridge". There are very few BLDC motor drivers in that power class or above, that are designed for Arduino control.
Wheel chair and mobility scooters use 24V DC motors pretty universally, and such motors are a few hundred watts typically. However burst power is usually quite a lot higher than continuous ratings to deal with climbing bumps and curbs. You'll find a lot of secondhand controllers for these devices in the 50 to 100A range.
Some motors will have a parking brake (electromagnetic solenoid clutch), which is also 24V and an amp or so. This needs to be energized before the motor can turn.
From the photo of the connector its possible your version is actually a BLDC rather than brushed motor as 3 high-current pins are visible - this will limit the kinds of controller that are appropriate.
Either way there are quite a few robotics motor controllers available for this sort of voltage and power.
Clearly a BLDC, the motor connector has 3 phase wires and 5 wires for the Hall sensors. You need a Hall-sensor BLDC motor controller with enough current handling.