Hi, I've found some problem in Agent API.
While the documentation is saying that
Retrieving the Available Skills
Returns the available skills to transfer a chat. The list includes all skills that have at least one agent online and is not currently engaged in the chat.
The request for the available skills returns all required skills except the chat-skill, the skill which is set for the chat-button in admin console and can be retrieve from agent API in visit session info.
This make impossible the transfer of the chat to the required skill (chat-skill).