If you are editing raw files then it isn't necessary to choose between the three choices. Your Lightroom and Camera Raw are current, so Lightroom just sends the raw data to Photoshop. Camera Raw converts it during the transfer. Make sure you use the "Save" option in Photoshop. Do not use "Save As". Try changing your sort order to "File name". Then the image returned from Photoshop should appear next to the original raw file.
Thanks for your answer.
I tried your proposals: right click on picture under lightroom, send it to PS, perform some modifications, and save picture. Close PS and get back to LR.
Picture is not here, even with the sort by name.
I checked in PS and can see the modified picture under recent files. The name is date-imagename.tiff in the same folder. And I'm still unable to get it back to LR even if I try to import it as LR says that the picture is already imported...
What am I missing ?
How would I say ? Huuuuuuuurraaaaaaaaaaaaaah
Many thanks for your answers to solve this issue. A filter I wasn't aware of ....