Farhad, you are wrong, and I think you have seriously misled this guy. Yours is very dangerous and very poor advice.

You are correct in that most inter-platform bridges are fixed on one and sliding on the other platform. However, movement of EITHER jacket due to wave load in the direction of the bridge axis will either COMPRESS or EXTEND the pipe between the two platforms. This is usually accommodated in loop arrangements. The worst case has to be both jackets moving exactly out of phase due to a large wave height, giving the maximum movement range and thus stress range. In my experience this has been as large as +/-750mm absorbed in loops.

Such massive movements will occur only due to large and infrequent waves, so contribute little to fatigue damage. Mid sized, high occurence waves will cause the most fatigue damage.

You should be thinking about a Miner's Rule assessment of fatigue life. Excellent guidance can be found in DnV documents.