What is the ruling on using a prayer bead with a thousand knots for tasbeeh, believing that Abu Hurayrah (may Allah be pleased with him) used to do so?

The questioner's mother has done well in her diligence concerning acts of worship. What she heard about Abu Hurairah (may Allah be pleased with him) is correct, for he had a thread with a thousand knots on which he used to glorify Allah. It was also narrated that he used to glorify Allah using pebbles or date pits. It is preferable to use the fingers for glorifying Allah, but the prayer beads (misbahah) are permissible.