Have you tried the CoordinateExtractor?

Yes, but CoordinateExtractor not generate CenterPoint of Lines or I don't know how. Documentation says that:

To retrieve the center point of a feature, use the CenterPointExtractor or CenterPointReplacer,

but for those transformers, I find information that works only for areas features.

Please correct me if I am wrong.

It will be a two step process, first find the center point your are interested in and then extract the coordinates of the point with the CoordinateExtractor.

Can you please explain what you mean by the center point of a line? Is it a point on the line exactly half way along the line?

Yes.

I found an alternative way to get center point of Lines (point located on line):

https://community.safe.com/s/question/0D54Q000080hZ36SAE/create-midpoint-of-every-line-feature (Takashi solution),

but still my question is not solved. IFMEPoint how to extract the values from Feature Information Window?

Could you perhaps post a screenshot of your workspace? I'd like to see where the CoordinateExtractor is located to see why that isn't giving you what you want.

I used parameter -0,5 and got INVALID_PARAMETER_INDEX

Could you share your workspace, how should I set CoordinateExtractor to recive CenterPoint on Lines?

If you are passing a point to the CoordinateExtractor set the mode to SpecifyCoordinate and leave the rest of the parameters as the default. This will put the coordinates into attributes _x, _y and _z.

But my input geometry is Line, not point. According to your proposition, I will get coordinates of Center of Point or start point of line not center point of line.

In my original approach, I have this coordinates as IFME Point information in Feature Information Window.

My major issue is how to extract information about coordinates from Snipper Transformer - from Feature Information Window.

Which transformer should be used to extract this information to attribute?

You said previously that "I found an alternative way to get center point of Lines (point located on line)" so you do have a point to pass to the CoordinateExtractor.