The article presents the challenges of introducing e-assessment at a traditional university where teachers did not extensively use online learning until the first wave of the COVID-19 epidemic. The ad hoc switch to online learning environments is known as emergency remote teaching because it was not planned. The first research supports other authors' findings that even teachers who already skilled ICT users in pedagogical practice faced some problems. Most of the challenges are related to exam proctoring. After a year of emergency remote teaching, the second survey results show a positive impact on education -- teachers became more confident, developed new teaching methods, and became more skilled ICT users. Teachers' exchanging of best practices seems to be an essential lever for the teachers' improvement. The cheating issues are still a focus.