I have seen something similar in a multi-period context, so I will have a go though I don't see the detailed calculation that Black and Litterman might have used.
Let me first invert the exchange rate and call it S, which now represents the price of one unit of other currencies in dollars (e.g., one pound equal S dollars). This is just to simplify the calculation.
The value of the unhedged portfolio at any time t will be $P_t S_t$. Let's first assume that we are investing for one period. We will be receiving $P_{t+1}$ units of say Pounds at time t+1, the dollar value of which will fluctuate, so to hedge we buy dollars forward at say $F_{t,t+1}$, which represents the forward price of one pound in dollars. But we need to hedge, say $P_t$ pounds, so we buy P contracts instead of one. Our hedged portfolio value at time $t+1$ would be:
$V_{t+1}=P_{t+1}S_{t+1}+P_t \left(F_{t,t+1}-S_{t+1} \right)$
Now lets consider multi-period and assume we keep rolling the forward hedge - we keep hedging one period ahead. The value of the portfolio after, say T period, would be:
$V_T=P_{T}S_{T}+\sum_{t=0}^{T-1}{P_{t} \left(F_{t,t+1}-S_{t+1} \right)}$
We would have funded the asset, but the foreign exchange hedge will be making or losing money, so there are a few alternative assumptions one can make - e.g., 1) the investment in the asset is reduced or increased by the amount of loss/gain on the currency hedge, 2) the interest rates are so low, and the net position will be small, so it won't make a difference, 3) we should account for the time value of money. I will go with the third and add the charge/reward for the balance in the hedge account:
$V_T=P_{T}S_{T}+\sum_{t=0}^{T-1}{P_{t} \left(F_{t,t+1}-S_{t+1} \right)\left( 1+R \right)^{T-t-1}}$
If you divide the above by the initial value of the portfolio, you shall get the formula in the form you have written. Notice I have inverted X so that is why you will see some differences.
So i can explain the 1+R in multi period settings but I am not sure if this is what the writers intended. Another potential explanation would be margining - collateralised trade or mark-to-market.