Hi Josul!

The first one is okay - "She is so happy because her sister is continuing learning English". A more natural sounding sentence is "She is so happy because is sister is continuing to learn English". To clarify, this sentence indicates that the subject's sister has not finished learning English, but is instead in the process of learning. If you want to say that the subject is happy because her sister learned to speak English, you would say "She is so happy because her sister learned English".

Hope this helps!