How could J1b arrive to Western Iberia ?
In terms of geographical curiosity J1b M365 linked Eastern and Western Iberia !
J1 M267 in Western Iberia could be related to several Eastern migrations or invasions since Prehistory. Iberomaurusian groups coming before the Neolithic, groups coming with the Neolithization of the Peninsula, groups arriving with early seafarers from Phoenicia or from Greece, Jews or Arabs could have brought some of the J1 M267 to Western Iberia. Every hypothesis is possible and must be tested.
The only organized migratory wave of people to Lusitania and Western Iberia coming from Eastern Anatolia and the Caucasus is the Alan movement in the fall of the Roman Empire.
One of the best compilations about the Alans is the book "Sources on the Alans" written by Agustí Alemany. Hydatius bishop of Aquae Flaviae (modern Chaves) wrote that in 409 the Alans led by Respendial settled in the provinces of Lusitania: "Alani Lusitaniam et Carthaginiensem provincias "
Jorge C. Arias thesis, Identity and Interaction: The Suevi and the Hispano-Romans, estimates the number of Alans in Iberia calculated in the literature as 30,000 to 40,000 people, so an organized influx of Caucasian DNA arriving in Western Iberia as a registered historical fact.
Portuguese Medieval genealogical records have names related to the Alans, like Mendo Alão (or Mendo Alam), a founding character of a Portuguese genealogical lineage and a mythical Armenian Princess too is present in the old legends.
Vestiges of the Alans in Portugal are also found in the legend of Coimbra's coat of arms, representing the Alan red lion and the Suebi green dragoon, according to Fray Bernardo de Brito in Monarquia Lusitana.
Respendial (Lusitania rex) was king of a group of Alans in Lusitania in the early 5th century CE.
Attaces, another Alan king in Lusitania (Ataces Lusitanae rex) was defeated and killed in battle with the Visigoths.
The first two kings in Lusitania were kings of Alan origin:
BERNARDO de Braga, O.S.B. ?-1605, Tratado sobre a precedencia do Reino de Portugal ao Reino de Napoles / composto por Frei Bernardo de Braga, copiado por Albano Antero da Silveira Pinto. - Porto : Typ. da Revista, 1843. - 54 p. ; 19 cm. - Copiado de um manuscrito autentico existente na Torre do Tombo
J1b M365+ in Western Iberia seems to be related to the Alan tribal migration of 409 and there's the possibility of a defined and recognizable haplotype (STR genetic signature) related to an Alan alpha male character in terms of a regular frequency and distribution in the modern Portuguese population.
More research is needed.