I can instantly tell that's fake. There's one word in there that tells me: "Sinnoh". See for instance Latias, which clearly says it has to be acquired by trading.
Just to give you an idea of the analysis, however, using Latias:
- Nature often doesn't tell anything, that's random even on Events except in scripted cases, like a Shiny Larvitar I have which MUST be Adamant.
- Date caught: also changes on imports between generations, means nothing and even DS dates can be wrong causing seeming irregularities that way.
- Location caught: One of the easiest ways to find fakes. If in that game or another across the set (B/W/B2/W2 happen to all share the set except in cases like Route 10, Challenger's Cave, and all B2/W2 exclusive locations), it'll show the catch location. If from an earlier game, it'll say generally only the region encountered. I identified a fake Jirachi and Arceus after the fact because both said "Johto" which is impossible. This location DOES NOT CHANGE; a Hoenn import eventually moved to Unova WILL STILL SAY HOENN (as well as having had a long travel through time).
- Met at level: Only conclusive if found at a level UNDER the minimum possible level, since you can't level down, UNLESS it's an Egg from a species that can breed, in which case it has hatch info.
- OT/ID: On Events, this can identify frauds if they differ from the real OT/ID with the Event. On catchable, usually your own OT. Jumping ahead to Lugia, I saw both share the same one. Instant suspicion without other proof.
- Exp. Points: Not usually something to look at, but in rare cases where it doesn't match the level (i.e. hacked to say Lv.100 but 10,000 experience points), it can be used as proof.
- HP/Attack/etc.: I don't use these, I don't know each Pokémon's average info. Many fakes can be identified by these numbers, however, and I know PokéCheck uses them somehow.
- Moves: If any move cannot be legitimately learned by the Pokémon or an evolution, it's a fake. This means either by leveling up, by TM, or by breeding (I hatched Squirtle with Brine and Aqua Tail for instance). There ARE exceptions, such as Dream World moves that are not learned any other way, or Event moves (Victini knowing V-create, or a certain Lv.100 Rayquaza also knowing it, but one caught in Hoenn cannot learn V-create). At first glance, these moves all match, but the Sinnoh bit invalidates it without coming down here.
Now, moving on to the Lugia: it's also fake. See Lugia. It can be caught via the Pal Park if caught in another generation, but it literally was an Event Pokémon in every way in that you need a MysticTicket to visit Navel Rock. And the catch location in B/W/B2/W2 would NOT say "Sinnoh".
I hope future generations retain catch location data in more detail to make fraud identification easier, but we know they'll not do that. However, BOTH of these are fakes. Delete both. :)