Unfortunately, you can see only the moves they made before the last deadline.
How to see other team’s transfers in FPL
1. Open the mini-league
Firstly, go to leagues and find a league where your rival’s team is.
2. Tap on transfers, next to their points
After tapping on transfers, the transfer history page appears, and you can easily check the transfers other teams made during the season. But you cannot see their current gameweek transfer and you can only check their transfers up to the last deadline.
You cannot spy on your FPL rivals anymore
In the past, it was possible to spy on your rivals, by checking the Finance and Transfers section in their FPL team. Their team value and money in the bank were calculated from all moves they made, so you could have guessed which transfer they made in any gameweek by observing changes in their team value.
However, this is no longer the case, and the team value you can see for your rivals in the team value from the last deadline.