In this situation, is the driver of the vehicle travelling in the right lane obliged to allow you change lanes?

In the photo there is a dual carriageway in a traffic jam, in the rain; you are driving in the left lane, which ends - on the left an area closed to traffic begins - and in the right lane there are a lorry and a white minibus with a trailer, which are not moving. The driver of the vehicle in the right lane is required to allow you to change lanes. The answer is: yes.

The Road Traffic Act states that when there is a significant reduction in speed on a roadway with more than one lane in the same direction, and it is not possible to continue in a lane because the lane ends, the driver of a vehicle in the neighbouring lane must, directly before the point where the lane ends, allow one vehicle from that lane to move into the neighbouring lane. You are in exactly this situation: traffic is at a standstill, your left lane ends at this point, and you are the first vehicle at its end. So the driver in the right lane is required to make room for you - this is not a favour from them, but the law. For your part, you signal the lane change with the right indicator, you do not force your way in, and you do not move over until you can see that the driver next to you really has slowed down.

Legal basis: Art. 22 para. 4a and 5 of the Road Traffic Act (Prawo o ruchu drogowym)