Is it considered unlawful or contrary to Sharia to request the written documentation of a verbal agreement, knowing that the lack of documentation could lead to legal accountability and harm to the association?

There is no religious prohibition in seeking that, nor is the one entrusted with the deposit obligated to accept it. However, if he accepts it without a written agreement, he has fulfilled his promise, especially if he incurs harm because of it. The harm incurred by either of the two associations, whether due to writing or not writing, must be considered.