Is it possible to install a RAM module from an identical PC into a PC with insufficient memory? They both have 507 MB at the moment. I have not checked to see if there are spare slots but assume that the memory will be interchangeable.
Assuming that you mean to say that both computers have 507MB (Non-standard size, are you sure? I'd have assumed 512MB but then when people were using MB for RAM I wasn't really that into computers) and also assuming that you mean that this memory is split into multiple card units, e.g. 2 256MB RAM cards per computers. Assuming that both of these assumptions are correct (Sorry, don't have the rep to comment so can't clarify), the computer you wish to transfer extra memory to also have additional free memory socket and the sockets and memory operate with the same interface, there is no reason why it wouldn't be possible to perform such a transferral.
To sum up basically you need to ensure that there are free RAM sockets on your mother board, that the memory you wish to install into the computer is compatible with the free sockets (A quick google search of the motherboard and RAM will easily tell you) and you're away!
Although you didn't explicitly ask for I'm going to give you a quick step run down. Firstly power down the computer and unplug it from the socket. Second, you should 'earth' yourself. The body can store a large amount of static electric which can instantly destroy delicate circuitry beyond repair if it were to discharge into it. So simply holding a radiator for a few seconds should do. Bear in mind that you will gather more charge as you rub against object even if you're only walking around, I'd advice using a static wristband and attaching it to a radiator so you're permanently earthed. Again one little discharge can render components useless. Lastly open the computers case and install the RAM (then put it back together obviously). Opening desktop cases is usually quite simple, just a couple of screws and/or clips. If they are laptops they are going to be very much more difficult to take apart, I cannot advise enough searching on-line for detailed video guides to taking your specific laptop apart.
EDIT Having just read that the two PCs are identical it seems that it would be a fair assumption that the RAM is compatible between the two devices. However bear in mind that often secondary RAM slots can sometimes have less capabilities. In other words the socket of the motherboard might be inferior to the RAM card in terms of buses and/or transferral speeds which could create issues.