There is a common misconception that one needs two most recent pay statements for H-1B transfers.
One of a common question I get around October 1st( since new cap H1’s start on Oct 1st) of every year revolves over how long does a person who has recently been granted a new H-1B status need to wait before one can transfer to a new employer. USCIS does not require two pay cycles to run before one can transfer. One can transfer immediately and there is no time limit. However one does need to show that until the day of filing of H-1B transfer one has maintained valid H-1B status as required. In summary if a new employee who has been granted H-1B status on October 1, 2018 decides to change their employer on October 10th, all one needs to prove is that valid status has been maintained from October 1st to 10th.
In summary, one does not need to wait for two pay cycles to change employment as it is a common misconception that one has to wait for two pay statements.