If you read the story, it says the investigator obtained the phone for further evidence, I would guess he continued to text her posing as the boy still before filing charges two days later.
Obviously the mother did not any longer have the phone since she handed it over to the police.. so how did she show the messages on the newsclip? My guess is she did not want to loose that evidence by turning it in, so as a backup she forwarded every message to her personal phone as backup for her own records. Thats why they say FWD on them. That is what I would have done, and likely anyone else so that to me would explain it.