Not sure it does what you want, but here is my proposition. It basically hands off any B message to A whenever possible, and checks the message has been sent after all:

class MessageWrapper
{
    object gate = new object();
    int? pendingB;

    public Message WrapA(int a, int millisecondsTimeout)
    {
        int? b;

        lock (gate)
        {
            b = pendingB;
            pendingB = null;
            Thread.Sleep(1); // yield. 1 seems the best value after some testing
        }

        return new Message(a, b);
    }

    public Message WrapB(int b, int millisecondsTimeout)
    {
        int? bb = b;

        lock (gate)
        {
            if (pendingB == null)
            {
                pendingB = b;
                bb = null;
            }
        }

        Thread.Sleep(3);

        if (bb == null)
        {
            lock (gate)
            {
                if (pendingB != null)
                {
                    bb = pendingB;
                    pendingB = null;
                }
            }
        }
        return new Message(null, bb);
    }
}