I would like to reply with my experience this week.
I did move that hive on Tuesday around 0930PM. Early next morning around 0600AM I went up and removed the moving screen and placed some branches all over the landing board. I stood and watched for a while as the first foragers came out. Well surprise, surprise, they did not re orient at all, but walked over the branches and flew straight out with a purpose. I watched for about 1/2 hour and many, many bees just flew straight out and did not stop to look around to re orient.
Well the next day I watched them fly over the old site all day and they also flew around the new site and around my other hive.
By Thursday evening at 0700PM when I went up to see how they were doing, well it was total chaos with bees flying everywhere and clustered all over the ground in back of the hives. They looked very confused and were shaking. I felt very bad about this and expected that I might have done something very bad. I posted this situation here on the forum and many members came forth to tell me that it can take a few days before the bees find their way to the new site. Other members said that a percentage of bees may never find their way back home again.
All is well for this hive now. All the bees have found their home again and everything is calmed down.
I am sharing this information so that you will not be alarmed if this happens to you when you move your hive. I just was not expecting something like this to happen.
Take care and good luck