
Quoting
Mr. Knowitall
As has been explained to you, even if your nominal salary is the same, unless your employer violates minimum wage laws you don't have recourse under wage and hour laws, although you may have recourse under contract law. The question of whether or not you have a contractual right to be paid for the two months at issue would require a review of your contract. Whatever the dates specified in the portion you're looking at, it may be that a full review of the current contract would reveal that the intent was to pay you from July, 2016 through August, 2017.
As your employer did compensate you for the two month "gap", even if by dividing your new contractual salary by 14 instead of by 12, your remedy lies in either convincing them to correct the injustice, or in trying to pursue a breach of contract case against your employer. Be forewarned that if you sue your employer for breach of contract, it's best to first have another job lined up.