Is it obligatory to inform the two partners about what the questioner did, regarding recording the value of goods at a higher price than what he purchased them for, knowing that he has relinquished two-thirds of what he receives from his share in the shop, and that what he left behind far exceeds what he gained?

If you have left for the two partners an amount equivalent to what you unjustly took from their money, then your conscience is cleared, and you are not required to disclose the truth of the matter. You are permitted to conceal your identity, provided that what you left for them was rightfully due to you, such as a known wage or your share of a profit that has already been realized.