Hi Maria,
If you go to the MSigDB Collections page, you can download the "json bundle" for each gene set collection. In that json file, each set has a "exactSource" key that has the Reactome pathway ID that you're looking for. Here's an example of an entry from that file:
"REACTOME_2_LTR_CIRCLE_FORMATION" : {"systematicName":"M26996","pmid":"","exactSource":"R-HSA-164843","geneSymbols":["BANF1","HMGA1","LIG4","PSIP1","XRCC4","XRCC5","XRCC6"],"msigdbURL":"
https://www.gsea-msigdb.org/gsea/msigdb/human/geneset/REACTOME_2_LTR_CIRCLE_FORMATION","externalDetailsURL":["
https://reactome.org/PathwayBrowser/#/R-HSA-164843","
https://www.reactome.org/content/detail/R-HSA-164843"],"filteredBySimilarity":[],"externalNamesForSimilarTerms":[],"collection":"C2:CP:REACTOME"},
-Anthony
Anthony S. Castanza, PhD
Curator, Molecular Signatures Database
Mesirov Lab, Department of Medicine
University of California, San Diego