You may need to write a formal letter of apology if you have stolen from a business, if it will prevent the business owner filing charges or to prevent further, disciplinary actions. You may also choose to write an apology letter yourself if you sincerely feel regretful towards the deed you've done. An apology letter should be typewritten.
Directly address the person or department you have wronged and start the letter by apologising for the inconvenience, expense, and time that was caused by the recipient(s).
Explain exactly what you did, even if the employer is already aware. Explaining what you did further shows that you are taking ownership and responsibility for the action. You may also choose to explain why you chose to make the decision to remove things from the business that did not belong to you.
List ways in which you intend to fix the problem. For example, if you stole office supplies you may choose to have the cost of the supplies taken out of your paycheck or pay them back directly.
Apologise again for the inconvenience that was caused by your actions. You may also choose to list your contact details and provide the recipient with an option for you both to sit down and discuss ways of remedy the situation.