What is the ruling on taking the increase offered in the value of the land, knowing that the initial agreement was not documented in writing and the sale of the land was delayed beyond the agreed-upon time?

It is permissible to sell your share of the land to your partner for any price you both agree upon, whether it is the market price, or less, or more. The mentioned increase is considered a permissible profit. Your partner is offering the market price, which is what you desire, and if you were to sell to someone else, he would have the right of pre-emption (shufa'a) for the same price. Pre-emption means that the partner takes what his co-partner sold by compulsion for the same price. The Hadith states that it is not permissible to sell a share in jointly owned property until the partner gives permission; if he agrees, he takes it, and if he dislikes it, he leaves it. Pre-emption is established for what has not been divided, but if it has been divided, there is no pre-emption.