Is there some reason to have the building block in a separate file?:

YES, I need to have the original template for the rest of the workers; each one of them works the template independently and they need to save the individual work in their own folders.

Is there a way to replace this line with this one, asking the user which path to save it to?

Marked bold line, replace

Application.Templates( _
"L:\06. MODELOS DE DOCUMENTOS\01 ATESTADOS\ACCIDENTES DE CIRCULACIÓN\BAEI\Informe Tecnico\BAEI - INFORME TÉCNICO.dotm"). _
BuildingBlockEntries("INICIO Y EXPOSICION DE HECHOS").Insert Where:=Selection.Range, RichText _
:=True

by this other line or something similar:

Application.Templates( _
"L:\02.- ATESTADOS 2022\ATESTADOS PAMPLONA\2. ACCIDENTES CIRCULACION" & AT-1234568 & "\BAEI – INFORME TECNICO.docm"). _
BuildingBlockEntries("INICIO Y EXPOSICION DE HECHOS").Insert Where:=Selection.Range, RichText _
:=True

AT-1234568 Name that the user is asked for, because I don't know what name he is going to give to that folder.