What you're showing and what you're saying don't add up. The pcb that you say is the original one has a single hall sensor, which can only be for speed measurement. You said it had three hall sensors!
If there were three hall sensors in the motor for positional feedback, you can normally see indications of the three positions where they sat in the slots of the stator. All you have to do is put three replacement bipolar hall sensors in there.
Sometimes you need a pull-up or pull-down resistor on the signal wire to ensure that they switch on and off. Good controllers have the resistors on the inputs, but some don't. In the case of the ones that don't, you can either install your own one or get a three hall pcb with resistors on it, but I can see that the one you got doesn't have resistors.
You can test whether you need resistors or not by connecting the halls to your controller, then check whether the signals pulse when you turn the motor backwards. You can only do that test when connected and the controller is powered. If they don't switch and stay 5v, you need pull-down resistors, and if they stay 0v, then you need pull-up resistors around 10K.