Is it permissible to accept money offered as personal assistance from another company that collaborates with the company I work for, without my employer's knowledge, given that I did not provide any assistance in this collaboration?

If the president of the second company offers the questioner a percentage of the profits due to his job position in his first company, then he is not permitted to take it except with the permission of his company; because it falls under the category of gifts to employees, and that is embezzlement (ghulul). However, if the percentage is offered regardless of his current job, then there is no harm in him taking it.