Transactions are verified before being added to a mempool. They are again verified before adding a block to a blockchain.
Can somebody explain me if in this step double-spending is checked or not ?
Yes.
If the transaction is valid -> add to mempool. If the transaction is invalid -> discard it.
If a transaction is recognized as a double spending transaction -> TX is not valid. Therefore it won't get added to the mempool.
For the future:
Please create a new thread if you have a question which is unrelated the OP or when the thread you want to post in is very old (1.5 years definitely is).
Necroposting in such a thread will just attract spammer.