Thank you for your reply!
Would you happen to know what 'recte KLINGER' means?
I saw this record, but I doubt that it's the right Juda Klinger as it seems that his wife's name was Ruchel / Ruchla. At least as per the record of marriage of one of his kids which I found in the archive of Paris.
On the other hand, I found another record, of birth, with same people - Juda Leib HORN recte KLINGER and Itte Leja HORN recte KLINGER - as parents of Jacob Mojzesz born on May 23, 1904 in Kolomyya (only 45 km / 28 miles from Kuty). As far as we know my husband's father's birth name was Mocek/Moshe Yacob Klinger but his self-declared birth date was August 3, 1905.
It's the closest I got so far, but it's not a perfect match :(
I attached the record of birth which I managed to download, in case you or someone else want to take a look.