Zakaah is due on sheep if they reach the nisaab or minimum threshold -- which is forty sheep -- and one full (Hijri) year has passed since they came into your possession, because of the hadeeth of Ibn Maajah (1792) from ‘Aaishah (may Allaah be pleased with her) who said: I heard the Messenger of Allaah (blessings and peace of Allaah be upon him) say: “There is no zakaah on wealth until one year has passed.” Classed as saheeh by al-Albaani in Irwa’ al-Ghaleel, no. 787.
The passage of one year is a condition of zakaah being obligatory on gold, silver, cash and an’aam animals (i.e., camels, cattle, sheep and goats).
If you ceased to own it before the year was completed, either because the property was destroyed or sold or given away and the like, then zakaah is not obligatory on it.
Based on that, zakaah is not due from your mother, because she ceased to own the sheep before one year was completed. And zakaah is not due from you for these sheep that you bought until one full year has passed from the time that you took possession of them.
And Allaah knows best.