Holmegaard Lutken Krystal Vase Etched, Signed Fake?

Hello, I am new to this forum and I'm very happy to have found it. I have a Holmegaard Signed small vase that I'm not sure about. I don't see a date, but I believe the mark is Per Lutken? It measures 4 1/2" tall, 3 1/2" diameter at largest point. This glass, however I have read that Lutken used thicker glass because it rarely bubbled, but this one has some tiny bubbles in it. Also, the stick on tag says: Kastrup-Holmegaard Krystal. Is Krystal the same as Crystal? Where my confusion comes in is the signature looks right, but so many of the attributes are not what I'm finding online. Any help will be very much appreciated! The nude lady on the vase looks like she is letting go of birds? Here are the photos:

It's from the 1957 'Susanne' series, produced until around 1976. The label on your vase dates its production to after 1965.

'15388' refers to Per Lütken's 'Hellas' vase, designed in 1950, which is the blank the motif is engraved on.

'3' refers to the engraved design (there were three designs in the 'Susanne' series).

I can't read the monogram at the end, but I seem to recall that the motifs were designed by Arne Bang, so it's possibly an 'AB'.

And, yes, 'krystal' is just Danish for 'crystal'.

Thank you so much Nic for all the great information!