What is the legitimate Sharia method for dividing the 6 million Algerian Dinars proceeds from the sale of a shop, given that the wife of one of the three brothers contributed 100,0 Algerian Dinars from her personal money towards its construction and furnishing, without any stipulations, knowing that the shop was purchased in 1992 for 110,0 Algerian Dinars?

If the wife paid money as a loan, she is only entitled to what she paid. If it was a partnership, then she is a partner according to her share of the capital and is entitled to a portion of the sale price commensurate with her ownership percentage.

If there was no agreement on a loan or a partnership, and no established custom, then the money is considered a loan, because merely paying the money does not make her a partner, and her right is established as a debt owed by the one who took the money from her (her husband).

It is advisable to document transactions to avoid disputes, and to be careful not to let worldly matters divide relatives. A solution that satisfies everyone can be reached by involving righteous people, and there is no harm in relinquishing some of one's right seeking Allah's reward.