You should have received a Frequently Asked Questions sheet with the request from the HSE for the schedule of assets.
What they are looking for is a copy of the Inland Revenue Affidavit (CA 24), which you or your solicitor completes as part of the probate process.
In some cases, if the value of the assets is low or if all assets were held jointly probate might not be necessary. If this is the case the HSE has a standard form to list the deceased persons assets, no solicitor is required. The HSE will send this form out on request.
The frequently asked questions sheet also says to contact them if you need assistance and they will help with any queries you might have.