Function LCS from qualV package (in Find common substrings between two character variables; not a possible duplicate) does something else than what you need. It solves the longest common subsequence problem, where subsequences are not required to occupy consecutive positions within the original sequences.
What you have is the longest common substring problem, for which you could use this algorithm, and here is the code assuming that there is a unique (in terms of length) longest common substring:
a <- "WWDUISBURG-HAMBORNS"
b <- "QQQQQQDUISBURG (-31.7.29)S"
A <- strsplit(a, "")[[1]]
B <- strsplit(b, "")[[1]]
L <- matrix(0, length(A), length(B))
ones <- which(outer(A, B, "=="), arr.ind = TRUE)
ones <- ones[order(ones[, 1]), ]
for(i in 1:nrow(ones)) {
v <- ones[i, , drop = FALSE]
L[v] <- ifelse(any(v == 1), 1, L[v - 1] + 1)
}
paste0(A[(-max(L) + 1):0 + which(L == max(L), arr.ind = TRUE)[1]], collapse = "")
# [1] "DUISBURG"
