When we convert from LIFO to FIFO, what is the reason for adding the LIFO reserve (net of tax) into equity? Thanks in advance

After thinking about it for a couple of minutes, here is what I came up with: The change in the LIFO reserve is the difference (LIFO COGS) - (FIFO COGS) for the period. The sum of all changes in the LIFO reserve over all years, which is equal to the LIFO reserve, is therefore the cumulative impact on COGS for all accounting periods so far. The LIFO reserve is therefore how much less we would have reported for COGS cumulatively so far => Subtract taxes and put into net income => FIFO Equity I’m pretty sure that I am correct in my reasoning but maybe someone can do a better job of explaining this

Your intuition is right. The LIFO reserve flows through the income statement so the reserve net of taxes is added to Net Income (i.e. Change in Net Assets) and therefore increases Equity on the Balance Sheet. Not much more to explain.