Hi. I transferred my embryos recently. The procedure is that the clinic releasing them hands them over to the transport person and witnesses a seal put over the tank. They sign saying this.
Then the transport person takes them to the receiving clinic and this person checks the seal is intact (each seal has a unique number is what I got told) and signs saying this.
I got an email from both clinics. The one that released them to say they were on their way and the one that received them saying they received them and confirming what they received. I don't know if they take them to the lab to check but I assume that's the case as they were very sure if what they were receiving.