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Given an input string, the Burrows-Wheeler Transform (BWT) can be seen as a reversible permutation of it that allows efficient compression and fast substring queries. Due to these properties, it has been widely applied in the analysis of genomic sequence data, enabling important tasks such as read alignment. Mantaci et al. [TCS2007] extended the notion of the BWT to a collection of strings by defining the extended Burrows-Wheeler Transform (eBWT). This definition requires no modification of the input collection, and has the property that the output is independent of the order of the strings in the collection. However, over the years, the term eBWT has been used more generally to describe any BWT of a collection of strings. The fundamental property of the original definition (i.e., the independence from the input order) is frequently disregarded. In this paper, we propose a simple linear-time algorithm for the construction of the original eBWT, which does not require the preprocessing of Bannai et al. [CPM 2021]. As a byproduct, we obtain the first linear-time algorithm for computing the BWT of a single string that uses neither an end-of-string symbol nor Lyndon rotations. We also combine our new eBWT construction with a variation of prefix-free parsing (PFP) [WABI 2019] to allow for construction of the eBWT on large collections of genomic sequences. We implement this combined algorithm (pfpebwt) and evaluate it on a collection of human chromosomes 19 from the 1,000 Genomes Project, on a collection of Salmonella genomes from GenomeTrakr, and on a collection of SARS-CoV2 genomes from EBI’s COVID-19 data portal. We demonstrate that pfpebwt is the fastest method for all collections, with a maximum speedup of 7.6x on the second best method. The peak memory is at most 2x larger than the second best method. Comparing with methods that are also, as our algorithm, able to report suffix array samples, we obtain a 57.1x improvement in peak.