What is the ruling on using work paper for personal photography and printing with the intention of compensating the user for it?

It is not permissible for an employee to use work tools, such as a photocopier, for personal use that has a significant impact, unless permission is granted, or if it is a minor matter that is customary. What is mentioned in the question is not minor, and its impact is strong; therefore, it is not permissible to do it without permission. Replacing the paper does not justify it, because the use includes the machine, its ink, and its paper. This is a betrayal of trust, which is forbidden in Islamic law, as Allah Almighty says: "O you who have believed, do not betray Allah and the Messenger or betray your trusts while you know [the consequence]."