如何在Interface派生类型之间进行转换？

interface InterfaceA
{
    string var1 { get; set; }
    string var2 { get; set; }
}

public class DerivedA : InterfaceA
{
    public string var1 { get; set; }
    public string var2 { get; set; }
}

public class DerivedB : InterfaceA
{
    public string var1 { get; set; }
    public string var2 { get; set; }
}

public class DoEverything
{
    InterfaceA A = new DerivedA();
    InterfaceA B = new DerivedB();

    A.var1 = "Test1";
    A.var2 = "Test2";

    B = ConvertObject<DerivedB>(A);

    write(B.var1 + ", " + B.var2);

    // This doesn't work, I would like it to though.
    public T ConvertObject<T>(object obj)
    {
        T result = (T)typeof(T).GetConstructor(new Type[] { }).Invoke(new object[] { });

        foreach (PropertyInfo propertyInfo in obj.GetType().GetProperties())
        {
            if (propertyInfo.CanRead)
            {
                try
                {
                    object value = propertyInfo.GetValue(obj, null);
                    propertyInfo.SetValue(result, value, null);
                }
                catch { }
            }
        }

        return result;
    }
}