This is tricky.

new String will never be interned if not interned explicitly, because it is, well, new-ed. So it's always new in the beginning, you will not get an interned instance by calling new (it can be interned later, but details are not simple). But. C# has the concept of operator overloading (unlike Java), and it overloads the operator == for many value types, including string. That's why str1 == str2 performs value equality check, and not a reference equality check. new String("") == "" will always return true. But. The example you showed does not perform a string equality check. It compares an object with a string, so the overloaded String.operator == does not kick in. The comparison is a reference equality check, and, in this case, it will return true only when checking equality of interned string instances.

Can somebody review my translation?)))

String.Join("", s) can be replaced with string.Concat(s)

And you do not have to apply splitEqually in movingShiftAux ;)