I would seek the advice of a tax professional. CPA, Attorney, Enrolled Agent, etc., who would be knowledgeable in this area. This is a complicated area of law.
Also, what form are the royalties reported on and what boxes are checked by the issuer/payer of the royalties? That has a bearing as well.
For some info, here are a couple of Pubs. Pub 559 indicates the inherited income is treated in the same manner as the decedent would have treated it. Look at income in respect of a decedent.
https://www.irs.gov/pub/irs-pdf/p559.pdf
Also look at Pub 525, Royalties. Second paragraph under royalties reads as follows:
In most cases, you report royalties on Schedule E (Form 1040). However, if you hold
an operating oil, gas, or mineral interest or are in business as a self-employed writer, inventor,
artist, etc., report your income and expenses on schedule C (Form 1040). (bold added by me)
A quick reading of this would tend to indicate that the royalties would be treated in the same manner as the decedent, and would therefore be put on Sch C. But, I would seek the advice of an expert in this area.