Zakah is due on sheep if they reach the nisab 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 Majah (1792) from ‘Aishah (may Allah be pleased with her) who said: I heard the Messenger of Allah (blessings and peace of Allah be upon him) say: “There is no zakah on wealth until one year has passed.” Classed as saheeh by al-Albani in Irwa’ al-Ghaleel, no. 787.
The passage of one year is a condition of zakah being obligatory on gold, silver, cash and an’am 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 zakah is not obligatory on it.
Based on that, zakah is not due from your mother, because she ceased to own the sheep before one year was completed. And zakah 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 Allah knows best.