Where can I find the following article, which concerns the n-queens problem?
E. Pauls, Das Maximalproblem der Damen auf dem Schachbrete, II, Deutsche Schachzeitung. Organ f¨ur das Gesammte Schachleben 29 (9)(1874) 257–267.
The only old documents I find available online from the Deutsche Schachzeitung periodical are from Volumes 20, 21, 44, 45, 56, 57, which are available at the Internet Archive. So if you really are after Pauls' exact article for historical reasons, you might have to track down a hard copy of Volume 29 at a library.
On the other hand, if you are primarily interested in the mathematical content of Pauls' article, then a decent (though also partial) exposition is available from "A survey of known results and research areas for n-queens" by Jordan Bell and Brett Stevens, in Discrete Mathematics Volume 309, pp.1-31 (2009). For instance, they spell out Pauls' method of proof for the existence of solutions to the n-queens problem (which appears in the first part of the article for which you want the second part):
Theorem (Pauls 1874). For all n>3, n non-attacking queens can be placed on the n x n standard chessboard.
The Bell--Stevens paper does point out that Pauls' part II gives a proof that the 92 solutions to the 8-queens problem given in 1850 by Nauck are exhaustive. But unfortunately, Pauls' method of proof isn't given. (That said, Pauls' work here is mentioned alongside Gauss' earlier claim that a brute force computation could be used to prove that 92 is the total number, so perhaps that gives a hint at how Pauls proceeds.)
Edited to add: Bell and Stevens do point to two other old secondary sources which they say offer "excellent summaries" of prior work done on the 8-queens problem. These are:
E. Lucas, Récréations mathématiques. 2ième éd., nouveau tirage. Librairie Scientifique et Technique Albert Blanchard, Paris, 1973.
T.B. Sprague, On the eight queens problem, Proc. Edinburgh Math. Soc., 17 (1899), pp. 43–68.
The first is available online via Gallica (see the section on "Le problème des huit reines"), but it appears not to discuss the work of Pauls; rather, it focuses on the work of Günther (S. Günther, Zur mathematischen Theorie des Schachbretts, Arch. Math. Phys., 56 (3) (1874), pp. 281–292), which work also receives an English-language exposition in an 1874 Philosophical Magazine article by Glaisher.
The Sprague piece is also available online, via Google Books, but sadly it doesn't address Pauls either; instead, it again offers a look more at the Günther/Glaisher work, but this does at least mean explicitly addressing the matter of the 92 8-queens solutions on the standard chessboard, among other things.