How to fix shifted axis after exporting from Blender?

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I have shifted axis on static mesh after export from Blender. Axis attached to the center of Blender scene. But object also has own axis. UE doesn’t understand it.

That’s how things work. The pivot point in UE4 is set to the world center from the blender scene.
While there are settings in the right button menu of the object placed in scene for Pivot Offset, but these are temporarily only.
Maybe you can change the Import Translation in the import settings, so that after a reimport the pivot is set to the place you want it to be.
Edit: there are pivot tools available on the UE4 marketplace - maybe that could help you.

There’s a plugin that comes with the UE, it’s called Modeling Tools Editor Mode. Among other things, it can easily manipulate pivots.