Is it unlawful for my husband's company to win a tender after lowering its price to become less than the other companies, knowing that the awarding entity prefers this company due to its familiarity with all projects and files, and my husband participated in reducing the price?

There is no blame on your husband if his company wins the tender, even if there is another bidder with a lower price. And there is no blame on him for reducing the price at the request of the company issuing the tender. It is not obligatory for the company to choose the lowest price; it may choose another due to trust or other similar reasons. There is nothing in the question that indicates bribery or deception.