STAR aligner is recommended for mapping QuantSeq FWD data. The reads may not land in the last exon and span a junction. STAR aligner can perform soft-clipping of the read ends during alignment, which can help maximize the unique alignment rate and avoids the need to trim additional 5' nucleotides prior to alignment.
Reads should however, always be trimmed prior to alignment to remove poly(A) tails and sequencing adapters (see What sequences should be trimmed ?. More information on QuantSeq FWD data analysis can be found here. Additionally, Lexogen has a web-based interactive platform for processing QuantSeq data. For more information, please visit our Data Analysis FAQs.