17th century Schleswig-Holstein Germany Beaker?

[legrandmogol]

I recently bought this old baroque cup that could be 17th or 18th century with at least 1 mystery mark. As far as I can tell it comes from Schleswig-Holstein but I am not too familiar with marks from this region. The makers mark appears to be UA but the U might be a different letter altogether. There is a much later engraving around the rim. Sadly the cup doesn't hold liquid any more thanks to an old repair that came undone Any help would be appreciated.

[Theoderich]

if the makersmark is (JA/S) then it could be Jürgen Anton Sebastian in Rinteln (Lower Saxony).
master ca.1669
+4.11.1723 (ca.80 Years old)

but this is a shot in the sky

[legrandmogol]

I think you're right about Rinteln rather than Schleswig-Holstein but not so sure about the maker