Initialize base class in .NET

Unfortunately base is readonly.

[Edit]
Well perhaps not so unfortunate. The relationship between a base class and a child class is IS-A not HAS-A. By allowing a child class to change the instance of the base class you are allowing the child class to change its own reference since it IS-A base class. If you truly need this functionality then I would suggest you change your inheritance model to reflect what you truly want to do.

Something like this:

public class A
{
    public string field1;
    public string field2;
}

public class B
{
    public string field3;
    public A a;

    public void Assign(A source)
    {
        this.a = source;
    }
}

seems more appropriate and has clearer meaning and functionality.

While there are many excellent answers here, I think the proper way to do this is by chaining the constructors:

public class A
{
    public string field1;
    public string field2;

    public A(string field1, string2 field2)
    {
         this.field1 = field1;
         this.field2 = field2;
    }
}

public class B : A
{
    public string field3;

    public B(string field1, string2 field2, string field3)
        : base(field1, field2)
    {
        this.field3 = field3;
    }
}

        public Assign(A a)
        {
            foreach (var prop in typeof(A).GetProperties())
            {
                this.GetType().GetProperty(prop.Name).SetValue(this, prop.GetValue(a, null),null);
            }
        }

Basically, it uses reflection to get all the properties of the base and assign the values of this, to all the values that exist in A.

EDIT: To all you naysayers out there, I quickly tested this now with a base class that had 100 integer variables. I then had this assign method in a subclass. It took 46 milliseconds to run. I don't know about you, but I'm totally fine with that.

No, the syntax you are trying is not possible. In C# .NET you need to do:

public void Assign(A source) {
    field1 = source.field1;
    field2 = source.field2; 
}