This is called parallelism.
The application of parallelism improves writing style and readability,
and is thought to make sentences easier to process.
You are asking if the second to is correct. Yes, that is correct. If the second to is removed, the sentence will also be correct, but defeats the practice of parallelism or balance in a sentence. You might want to read the short article in Wikipedia to understand more the concept of parallelism.
Just want to share... If you are not very keen with the sentence, you would not even notice it. I know a lot of people who do not practice parallelism because I read emails everyday. However, I recommend that you put parallelism into use always.