Is it permissible to deduct a larger amount from the share of an heir residing outside the country in an inheritance inventory transaction, or should the expenses and lawyer's fees be deducted from the total estate and then distributed among the heirs according to Islamic law?

The resident outside the country receives his full legal share. The principle is that the costs paid for the inventory of the inheritance should be borne by the heirs in proportion to their shares in the inheritance, because the expenses for partners are in proportion to their shares. If the residence of the person outside the country has an impact on increasing the inventory costs (such as external authentication fees), then he bears those additional costs specific to him.