Who should specify user stories in details?

The Product Owner is accountable for creating, ordering, and communicating Product Backlog Items. Even though the Product Owner is accountable, some of the work may be delegated. For example, if there are known defects, expressing those defects as Product Backlog Items and suggesting an ordering for them may fall to test or product support specialists, but the Product Owner would be accountable to ensure that they are created properly (however the team defines properly) and are ordered appropriately with the rests of the work.

The majority of the work in clarifying Product Backlog Items, which may result in creating new (smaller) Product Backlog Items comes through the process of Product Backlog Refinement. Refinement is an ongoing activity that both the Product Owner and the Developers participate in. There are plenty of ways to go about refinement, but that's up to the team (perhaps with coaching from the Scrum Master) to figure out. 

Since the Scrum framework only has roles of "Product Owner", "Developer", and "Scrum Master", it's difficult to talk about who participates in refinement from your organizational roles. Some organizations do have specialists, such as analysts, test specialists, and similar. These may be Developers, in which case they would take part in refinement activities. In the end, the whole team would be involved, in some way, in making sure that the Product Backlog Items have enough details to allow work to proceed.

I would recommend caution when thinking about specifying anything "in as much detail as possible". Specifying work in as much detail as possible is often costly. It also reduces feedback cycles on working product. Specifying just enough detail to allow the team to understand the work, ensure it is well refined (for example, small enough to deliver within a Sprint) would be better. The risk tolerance of the organization would be a factor as well - risk-adverse organizations may spend more time in up-front refinement activities than risk-tolerant organizations to ensure that the work is clearer and well-understood.

I have question about creating user stories. I know that responsible is PO,

The Product Owner is accountable.

but she/he can generate ideas and delegate the rest of the work to others (In the rest of the work, I mean specifying user stories in as much detail as possible, shortly technical part).

I'd suggest it may be better to specify items with as little detail as possible, so as to leverage the creative potential of the Developers to the maximum.

From team who can do this part of the job?

Given that the PO will remain accountable, who would he or she trust most?