If you are working on a raw image, and Lightroom and Photoshop are both up to date, when you choose to edit in Photoshop you shouldn't see the choice to edit a copy with Lightroom adjustments. Lightroom should simply pass the edited raw file to Photoshop without any prompting whatsoever.
The answer is perfectly correct.
But my problem is, in my case- this does not happen--" Lightroom should simply pass the edited raw file to Photoshop without any prompting whatsoever."
The photoshop and the LR are in a great tango each enjoying the latest icings and Camera Raws to compliment but the corrections in the LR won't travel to the Photoshop. The file drops all the attire and goes naked to Photoshop.
I cannot replicate your phenomenon on my Windows 10 computer using Lightroom Classic CC 7.3 and Photoshop.
Even Adobe does not understand why it is happening, ---when---- the same LR version with the Photoshop version of 2017 ( version 2017.1.2 release) Camera Raw 10.3.0.933 plays sans problem. Which means the 2018 update of the PS Classic has some bugs and clash with WIN 10 Home Edition that they need to address?!
All my guess-- could be off the track by miles.