When an identity thief creates false e-mails and/or websites that look legitimate but are designed to gain illegal access to a victim's personal information, it is called:

The correct answer is "Phishing".

Explanation:

When someone engages in activities as described in the question, this is called "Phishing". Phishing can be done by sending email or texts that are made to look like coming from a trusted source. When the victim engages with these, usually by clicking a link, it leads to the installation of malware which can be used to copy personal information such as credit card numbers, passwords etc. I hope this answer helps.