gistfile1.cs

public class ClassA
{
    public Task TheTask;
    public string Result;

    public ClassA()
    {
        TheTask = SomeLongMethod();
    }

    private async Task SomeLongMethod()
    {
        // Run the CPU-blocking method on another thread and wait for the result
        // This does not block the main thread.
        Result = await Task.Run(() => Test());
    }

    public string Test()
    {
        // Do some CPU-blocking work
        Thread.Sleep(1000);
        return DateTime.Now.ToString("HH:mm:ss.ffff");
    }
}

public class ClassB
{
    public string Test(ClassA a)
    {
        // Simulate the time between ClassA is instantiated
        // and the result of the task is actually needed.
        Thread.Sleep(1000);

        // Wait the remaining time of the task.
        a.TheTask.Wait();

        // Use the result of the task stored in the other field.
        return a.Result;
    }
}

public class Program
{
    private ClassA a;
    public Program()
    {
        a = new ClassA();
    }

    public async Task Main(string[] args)
    {
        var b = new ClassB();
        string res = b.Test(a);
        Console.WriteLine(res);
    }
}