"Can I get a help with a letter from IRS, correcting incomes from securities for RSU sell-to-cover sales? I did not sell any vested shares."
The terminology "sell-to-cover" refers to a situation where something vests - shares of your employer in this case - and simultaneously some of those shares are sold. The cash raised by the sale those shares goes back to the employer either to cover the exercise price (e.g., you exercised a typical Non-Qualified Stock Option) and/or to cover the taxes created by the exercise or vesting.
In the case of an RSU the shares that vest are legally yours the second they vest, so any sell-to-cover activity means that you sold the shares, even if you didn't pick up the phone, call the broker, and say "sell". If you received a 1099-B and didn't report that sale on your income tax return, thinking that it wasn't necessary, and the IRS is now questioning you about the "missing" 1099-B then you can either amend your income tax return to include the sale, (a "same day" sale typically results in a small loss due to selling commissions and fees, so you might be due a small refund), or you can explain the situation to the IRS in a letter, indicating that including the 1099-B would not cause you to owe additional taxes. The letter probably indicates your course of action.
