Mostly it should work, at least for a while. There are some things that won't work at all: As you said the speakers won't work and as the oscillation of the membrane is not damped by air anymore, trying to use them might break them easily. Then the acceleration sensors will not work as intended, because the phone cannot determine its orientation by measuring gravity. This might mess with the user interface or some controls. Last, you are not going to get any signal unless you place a relay nearby.
I don't see any other function that would not work at all, but there will be issues limiting the lifetime of the phone. The first one is heat. Usually the phone is cooled by convection in air, which won't work in a vacuum. If no alternate means of cooling is provided, the phone might overheat quickly. So you would need to cool it somehow.
Then there is radiation. If the electronics are not radiation hardened (and I don't see why the designers should have cared for that) and they are placed outside the van Allen belt they will fail sooner or later due to degradation by radiation. If the phone is supposed to be operated by humans, they will also suffer the radiation, so it would be in their interest to minimize radiation, anyway.
The limiting factor will be outgassing. All materials will slowly evaporate when placed in a vacuum. For most metals this will be very slow, but some polymers have a high outgassing rate. If the rate is too high, the material will evaporate until there is nothing left anymore. And if this material had a critical function, the phone will fail when it's gone. How long this would take depends on the materials used and their function.