Hope you all are doing well

My employer has contacted me, stating that I will be furloughed for the month of May. However, he will top-up the furlough scheme payment so my salary won't be effected, and I will receive 100% of the salary mentioned in my CoS.
My questions:
1. I understand that furlough scheme is not considered a public fund. But would there be any impact on my current tier 2 visa, or future ILR application?
2. Should my employer notify home office of me being furloughed? Or is it irrelevant as long as my salary is still the same?
Best,