To solve this question, the user needs to know the differences between the concrete implementations of the Map interface and their iteration orders.

Now, let's go through each option and explain why it is right or wrong:

A. TreeMap: This option is incorrect because TreeMap sorts its elements in natural order or by a custom Comparator, whereas the iteration order of the existing instance of the Map may not be sorted. Thus, creating a new instance of TreeMap would not preserve the same iteration order as the existing instance.

B. HashMap: This option is incorrect because HashMap does not guarantee any particular iteration order. Thus, creating a new instance of HashMap would not preserve the same iteration order as the existing instance.

C. LinkedHashMap: This option is correct. LinkedHashMap is similar to HashMap but maintains a doubly-linked list running through all its entries, which allows it to maintain the insertion order. Thus, creating a new instance of LinkedHashMap would preserve the same iteration order as the existing instance.

D. The answer depends on the implementation of the existing instance: This option is incorrect because the iteration order of the existing instance of the Map may not be guaranteed by all implementations of the Map interface. Thus, it is not a reliable solution to assume that any implementation of the Map interface would preserve the same iteration order as the existing instance.

The Answer is: C. LinkedHashMap