Is Amr entitled to claim his money from Zayd, and is what transpired between them a Mudarabah or an Inan partnership? And is Zayd obligated to return all, some, or none of the money after his loss?

First: The difference between mudarabah (profit-sharing) and 'inan (partnership) is that in the former, capital comes from one party and labor from the other, whereas in the latter, both capital and labor come from both parties, or labor from one of them. This does not change the ruling that a partner is a trustee (amin) who is not liable except in cases of transgression (ta'addi) or negligence (tafrit). His word is to be accepted under oath regarding profit, loss, and the loss of capital.

Second: The fleeing partner is liable for the capital due to his transgression. As for the other partner, "Zayd," he is not liable for people's money unless there was transgression or negligence on his part. Among the forms of negligence that necessitate liability are: not informing the other partner, "Amr," that there is a partner who has control over the money; or if Zayd guaranteed his partner in the event of his transgression; or if he concealed the news of his partner's transgression against the money. If there was no negligence on Zayd's part, then he is not liable for anything, and everyone should demand from the fleeing partner what he took.