So my niece is going through?

My 16 year old niece should be 11 weeks and 2 days today but Saturday she went to the hospital Saturday night due to bleeding they checked her hcg levels and they said it looked fine. They did a sonogram and the baby only measured 8 weeks, and that she was going through a spontaneous miscarriage. She is suppose to make an appointment this this certain Doctor but is refusing to go. So today she calls me and says her boyfriend sister had went to the same hospital as her and they had told her that she was having a mc and she ended up giving birth couple months later. So now she thinks that she might still be pregnant and the hospital was wrong bc they said her levels looked good. I did explain to her that the only way they will know for sure is if they recheck then within 48 hr to see if they were doubling. and that its not good that the baby only measured 8 weeks when she was suppose to be 11 weeks. I asked her if they saw a hb and she stated they didn't let her know anything about that. So she took a test today and it was positive I did advice her that hcg levels will still be present even when she is miscarrying. My question is will a test still show up positive even if the baby passed 3 weeks ago? Also has anyone been told they were having a miscarriage but sill had a healthy baby. I had adviced her to go for a second opinion if she has doubt but said she wants to wait it out. Thank you