Can I connect two separate ducts systems together?
It won't hurt anything as a temporary fix. The existing one side of the AC system will have about the same cooling capacity, but each side of the apartment will now have one-half the cooling capacity, assuming the same amount of air is delivered to each side which is unlikely given the extension and turns needed to jumper to the other side (extra pressure drop). The AC will run longer, and will probably not even meet the thermostat set point so will run continuously. If it does ever turn off, say at night, at least the system hit the Tstat set point. This could also result in the tenants on the good AC side complaining since there will be less cooling there. I agree with @Michael Karas, get the broken one fixed as soon as possible to avoid the extra work. If you choose to do this, and this duct is out of sight, put a damper in the extension so you can open/close as needed in the future. Replace the filter at the bottom of the broken unit with cardboard to restrict air from flowing backwards through the broken unit.