I have an equity transaction of 100,000 (GBP) in January 2021. To get the consolidated balance sheet for October 2022 to the American parent, do I use the historical rate in the consolidatedexchangerate table for October 2022 from the British subsidiary to the American one or the one from the date of the transaction (January 2022)?

If the account type is historical, you use the Jan 2022 historical rate on this transaction (if you have other additional transactions, you use the rate of the posting period for each transaction to get your grand total) If the account type is current, you use the Oct 2022 current rate on the full balance of the account