Transmission on the right RF frequency is one item, you can check whether your available senders are accepted by your receiver.
Another item is the data format, sent by the old sensor and expected by the home station. This can be any binary stream, and you're almost lost without a second (working) sensor, from which the data format could be determined. Also the transmission mode has to be determined, does the sensor send at regular intervals, or only when asked for by the base station?
The simplest solution were finding out the failing part of the outdoor station, and if it's the humidity sensor or the sender, replace it by some commonly available one.