Q: Can I make an inquiry if the 'Reviewers invited' status has lasted a month?

Yes, you may mail the editor seeking an update. A month is a rather long time for the manuscript to be stuck at the Reviewers Invited stage.

However, there are a few points that are not entirely clear in your question, which may determine how long the wait for the reviewers and the review process may actually end up being.

You have said that you sent a list of recommended reviewers to the journal and the initial review was completed in a short time. By this initial review, if you meant the initial admin check, that does take a short while.

If however you meant that your manuscript went through an initial peer review (with the reviewers from your list) and then the editor decided on sending it to an additional two reviewers (of their choice), this may mean that the peer review process, in a way, has only begun. If this has indeed been the case, the editor may not have been entirely convinced by the reviews done by the reviewers you shared.

Again, if this is the case, it would be best to also seek clarification on this when you mail the editor about the delay/status.

As this might be a tricky piece of communication to write, you may refer to the templates provided in this handbook: A practical handbook of templates for communicating with the journal [It’s by R Upskill, a sister brand providing learning programs for a variety of researcher needs, from writing to handling peer review to publication and even to promotion. You may visit the site to know more.]

Hope that helps. All the best for the next updates on your paper!