[MrMon]

I'll just hazard a guess that the final successor corporation is whoever is the local phone service provider now. If any stock from that era has a chance of being worth something, it's probably a telephone stock or similar utility. Utilities usually don't go under, and my guess is that it was bought out as service consolidated. So it might be easier to start with the existing company and work backwards. Or use your grandmother's memory and see how far back she can remember the providers.

Also, don't dismiss the one share at $10. That was a whole lot of money back then and given the power of compound interest, it's potentially worth quite a bit. 3% for 104 years is $216, 5% is $1,598, and 7% is $11,374.