Does the ruling on the widespread effect of manumission differ if partners are of different faiths?

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There is no distinction regarding this ruling whether the partners are Muslims, disbelievers, or a mixture of both. This is the position of Ash-Shafi'i. The rationale is that the ruling generally aims to remove harm, which applies equally to Muslims and disbelievers, similar to returning goods due to defect. The primary goal here is completing the manumission and repelling harm from the co-owner, not establishing ownership, which distinguishes it from a sale transaction.