Everything was deduced by Shire and Lucia based on the situation in Brute Village.
The "Lady in White" originated from the intelligence agency in Belgium, and Ypres is a Belgian town. It is reasonable that Lucia would know and analyze these things.
One day, if someone ever questioned Shire because of this, the "Lady in White" and many Belgians who have seen the situation in Brute Village could testify for Shire.
But of course, currently, Shire does not need to go out of his way to prove his innocence.
He immediately returned to headquarters to inform Gallieni of the intelligence and his speculations.
In fact, Gallieni knew that Shire had an intelligence network in Belgium.
Although Shire kept it a secret from everyone, many people knew: because Shire saved Belgium, the Belgians spontaneously organized an intelligence agency to be loyal to Shire.
