A Store Owned by Partners, When One of Them is Sitting Shiva

In a store owned by partners, if one of them is sitting shiva for his father, is it permissible for the partner to open the store during the shiva period?

In a store owned by partners where one of them is in mourning, it is forbidden to open the store during the first three days, even if the mourner foregoes his share. From the fourth day of his mourning, it is customary to be lenient, allowing the partner to open the business.

The Talmud in Moed Katan 11b discusses a case where two individuals had a team of oxen. When a relative of one of them passed away, he did not send his ox to work. Rav Ashi questioned this, arguing that while he may not be concerned about his own loss, should he not be concerned about the loss of the other? This implies that the partner of the mourner should not have to cease work because of him unless he is an important person.
In the Jerusalem Talmud, Moed Katan 3:5, it is stated: “two brothers, two partners, two slaughterers, two storeowners, if a thing (a death in the family) happened to one of them, they close up their shop. But their hired workers and contractors are allowed to work surreptitiously in a different place.” This implies that the partner of the mourner does not work in the partnership during the days of his mourning.
The Rif and Rambam ruled like the Jerusalem Talmud that the partner does not engage in work at all, while the Raavad and Ramban wrote that the Jerusalem Talmud speaks about public work and the Babylonian Talmud about private work, hence the partner works privately and not publicly. In the case of a important person, even private work is forbidden as it will be said that he is working during his mourning days.
Practical Halachah: The Shulchan Aruch (Yoreh Deah 380:21) writes that if one of two store-owning partners experiences a bereavement, they close their store, so the partner does not work publicly. However, he can work privately in his home, even on the partnership business. If the mourner is a important person and the partnership is known by his name, it is forbidden for the second partner to work even in his home.
The Mishkenot Yaakov (Yoreh Deah 68) cited in Pitchei Teshuva (Yoreh Deah 380:5) ruled like the Rif and Rambam.
The Chochmat Adam (134:16) wrote that the custom has become to be lenient after three days. However, in his opinion, this applies specifically from the fourth day onwards. The Mishnah Berurah (548:24) concurs with this view.