Is accounting in US dollars, while receiving payments in Russian rubles and recording them in US dollars, permissible or impermissible (halal or haram)?

What you take in Russian currency is considered a money exchange (sarf) for what your associate owes you in dollars as your wages. The exchange rate of the dollar against the Russian currency at the time of receiving the payment must be known, because a condition for the validity of a money exchange is that it be immediate. It is permissible to exchange fixed currencies that are a debt in obligation if it leads to the fulfillment and extinguishing of both debts. It is permissible for the creditor to collect his debt in another currency, provided that the payment is made immediately at its exchange rate on the day of payment. This is supported by what Ahmad and the four Sunan compilers narrated from Ibn Umar – may Allah be pleased with them both – who said: I came to the Prophet, peace and blessings be upon him, and said: "I sell camels in Al-Baqi', and I sell for dinars and take dirhams, and I sell for dirhams and take dinars." The Prophet, peace and blessings be upon him, said to him: "There is no harm in taking at the rate of its day, as long as you do not separate with anything remaining between you." Also, the resolution of the Islamic Fiqh Academy states the permissibility of the creditor and debtor agreeing on the day of payment—not before—to settle the debt in a currency different from the debt's currency at its exchange rate on the day of payment, provided that nothing remains in the debtor's obligation from what was exchanged. Therefore, the considered exchange rate is the rate on the day of payment.