Is it permissible to sell a book through a center for teaching the Quran to foreign students, whereby the seller receives a percentage of the profits in local currency, knowing that the purpose of this is to avoid problems proving the source of income to banks, and is this considered a trick to circumvent the unlawful?

If the center sells the book in a lawful manner, then there is no objection for the questioner to contract with them to sell her book, as it is permissible for her to sell it to the center, or to share in its sale with them, or to appoint them as agents for its sale. The principle in this regard is that a stratagem (hila) is permissible if its means are lawful and it leads to a lawful outcome. This falls under the category of stratagems where the method is lawful and what it leads to is lawful, such as selling and agency, which aim to bring benefits or ward off harms.