depreciation on gift rental property

My mom want to transfer her rental property to me so I can manage it and also receive the rental income. To my understanding, this is considered her gift to me, and I need to file tax for the rental income on schedule E and deduct the expenses.

I have question on the depreciation. Will I continue to use my mom's cost basis and carry over her depreciation for the remaining years as well? Or I need to figure out the new cost basis at the time of transfer and if so, do I need to deduct her accumulated depreciation to figure out the new cost basis for depreciation.

As for my mom, will she just stop claiming this property on her tax return or is there extra step she needs to do on her tax return?

Thank you in advance for your advice and opinion.