The Analog In does exactly what it says - it only reads (samples) analog voltage levels.
Using AnalogWrite(0,2) does not make pin A0 in Analog In to output the voltage of 2*AVCC/1024, but instead makes the pin D0 to do that instead. (Most D0 pins on Arduino boards do not have a PWM output associated with them, so the behaviour would be undefined.) In the mean time, your A0 is doing nothing.
(I suspect it's floating / not connected, hence the 3xx value. Could check the datasheet to be sure.)
So what should we do instead? For a start, connect Arduino B's A0 to Arduino A's pwm pin. If you're using Uno, you can connect to any of the pins 11,10,9,6,5,3. Then you can use the code:
int PWMPin = 11;
int SignalLvl = 2;
Give that a try. And you'll see that it works... sort of.
But then there's a problem. your readings will be close to what you want, but quite erratic. The reason is partly because analog signals are super unreliable and is filled with noise. But the main reason is really that Arduino's analogWrite is actually NOT designed as an analog signal output. It is a PWM, which outputs GND and AVcc levels at variable periods at a fast speed so that it approximates the voltage level you want when averaged.
If you want to experiment with this, you can connect a resistor and capacitor to the output, creating a low pass filter. (Here's more info: http://provideyourown.com/2011/analogwrite-convert-pwm-to-voltage/)
Having said all that, I guess the question most of us would like to ask is: is there a reason why you want to send data via analog? Analog signals are prone to noise. If data fidelity is critical, your best best is to use serial communication as highlighted by most answers here.
For simplicity, I suggest I2c which uses only 2 wires to communicate. If speed is of essence (like, writing to 10,000 bytes of data every second) you could try SPI or even parallel communication.
Hope this helps and good luck!