I am looking for Mouse Ensembl Gene ID Human Orthologs MSigDB.v2022.1.Hs.chip(a chip file for GSEA test). The MSigDB database direct me to Alliance of Genome Resources database. When I typed down the key word, I didn't find the chip file that I need. Does anyone happen to know where I can download the chip file with that typical version?

This support site is meant to help people with questions concerning Bioconductor software. It's not clear to me that you are asking anything about a Bioconductor package (and please note that by adding the DESeq2 tag you are unnecessarily pinging Mike Love, who is the maintainer for that package, which 100% has nothing to do with GSEA, so you are bothering somebody who cannot possibly be expected to provide help). In future, if you have general questions like this, ask over on biostars.org instead.

To your question, I believe you are misunderstanding what you read on the Broad MSigDB site. They aren't saying that you should go to a different website (they are saying that they have used updated information FROM that website). The direct link to the file(s) you want is here.