Höfner was founded in 1887 by Karl Höfner in Schönbach in what is now the Czech Republic. In the beginning then made Violins but as the Company grew so did the range of instruments they made. By the mid 1930's is was a large operation with over 300 employees. After WW2 the German speaking workforce was deported to Moehrendorf including, in 1946, one of Karl's sons who either worked for or helped set up, (depending on which history you read?), Framus. By 1948 all of the Höfner Family including Karl had relocated to Moehrendorf and a new Höfner company arose to compete with Framus. Höfner suffered against Far Eastern competition through the 70's and 80's, (by now it was being run by Karl's Granddaughter), until in 1994 it was sold to Boosey & Hawkes. By 2004 Höfner had been sold on to its senior managers and its still in business making electric Guitars today. 

That history is easy to find but its history of Ukulele making specifically is much harder to give firm details on. There was a page of Ukuleles and a page of Banjoleles in the 1937 Catalogue with the banjoleles particularly looking like the no-name bracketless banjoleles that were seen being sold cheaply in this period. Ukuleles also featured in the 1963 and 1973 catalogues. I've never seen even a photo that can definitely be said to be a Höfner produced Ukulele from this period, just the catalogues. The few photos you do see of Höfner Ukuleles are clearly Brüko Ukuleles that have had a Höfner label put in, (though the pictures in the later catalogues don't illustrate Brükos?) and the 2003 Ukulele I have a photo of, looks like a re-branded Gewa? 

In 2013 they reintroduced a, (Far Eastern made), Soprano, Concert and Tenor spruce top, mahogany Ukulele they call the "Sunset" range but these have now been discontinued

Höfner have for some time distributed, (possibly even owned), a Spanish brand of Guitar called Carmencita and today these guitars are still in the catalogue. Höfner only acknowledge this Spanish produced guitar and I can find nothing to suggest Höfner had anything to do with the Teisco made Carmencita instruments including a Baritone Ukulele distributed in the USA in the 1960's. The name itself has existed for a long time with an appearance on Mandolins in The Tonk Bros 1903 catalogue?