There is one episode in Kamen Rider W in which Shroud mentioned Philip that she knows the Narumi Detective Agency's underground before he came to the place. I think this clip might be a proof on what she said.
If I would tie in the rumors and the facts mentioned in the series itself, I think this pic above might happen before Begins Night started. It was stated at the finale of the series that it was Shroud who hired Sokichi. Also, there can be another interpretation on this scene.
Since Shroud's hair is short and the possibility that it is still a couple of years after she was burned by Ryubee, we might say this scene might be a scene regarding Sokichi obtaining his Skull Memory and Lost Driver.
Note: Until there is a confirmation coming from Toei about this scene, there are a lot of possible interpretations on this. Its up to you on how you see it.
Pic courtesy of: alternate-zer0