I need to transfer x amount of cryptocurrencies (like bitcoin, ethereum, kbc) programmatically from one wallet to another. Then, I need to verify if the sender sent the money to the address of the recipient's wallet.
Is there any library for doing that? Is there any documented api on any web services?
I think you are looking for services like Shapeshift or alternatives.
There are a bunch over https://news.bitcoin.com/four-alternatives-to-shapeshift/. For some of them, you'll have to do some KYC.
If what you wanted to achieve is only to send a transaction to move funds within the same blockchain, I would suggest using APIs to push&monitor transactions to do so.
ETH: https://infura.io/docs BTC: https://www.blockchain.com/api