Voynich buys some Jesuit manuscripts

[Scarecrow]

It seems to be also quite sure, that it was father Joseph Strickland who transferred those manuscripts (listed in the APUG 3289) to Villa Mondragone in Frascati.

No, there is no evidence of this.

Some evidence at least but no smoking-gun. 
In the study there is written (page 345) that Strickland is implicated as from the "diary of the house" and from the "registry of the spending" of Castel Gandolfo, that he went for two "lunch" meetings at villa Torlonia, and as Strickland was resident of villa Mondragone, these visits may implicate that he did move manuscripts between the two places.

It seems that the APUG 3289 has been compiled by.. the belgian jesuite Pierre-Jan Beckx.

I also don't think that that is correct. 

At page 339 they study says, regarding th APUG3289, that according to the research of Francesca Niutta, the index has been connected to Beckx.
"Secondo la convincente ricostruzione di FrancescaNiutta, l’indice andrebbe fatto risalire al gesuita belga Pierre-Jean Beckx (1795 - 1887), il quale, preposito generale della Compagnia di Gesù dal 1853"

It remains a matter of guesswork why Ethel mentioned Frascati.

Yes.