Is it permissible to use stationery that a father brings home from his workplace, which is owned by the company, whether for personal use at home or for da'wah activities at the mosque, especially if it would be damaged by being left behind?

If a father brings items from work without permission, it is not permissible to benefit from them, and the father must be advised to return them. If he does not, you are obliged to return them if possible. However, if he is authorized to bring them for use in his work, you are not permitted to use any surplus without explicit or customary permission; otherwise, they must be returned to the concerned party. But if the workplace has discarded them and neglected them, then there is no harm in benefiting from them.