The virus remains in one's body forever, based on everything that I have read. Your BF has it too although there is no test for men besides a biopsy of a genital wart. He has to accept the odds (99%) that he has what you has despite not getting a medical diagnosis. There is no ping pong effect. Your GYN should advise you what to do since you are pregnant. If there are genital warts, then you may have to get them removed. If it is a high risk strain (no warts), then your GYN will know whether to do a procedure or not while pregnant.
Don't worry about who gave it to who. It doesn't matter anymore. You two cannot re-infect each other but you can infect others who are not already infected with your strain. You two can have all of the unsafe sex you want forever. Condoms are not needed except to prevent another pregnancy or to prevent other STDs if you or he sees other people.
Read the link below to educate yourself. The high risk for cancer strains are the ones you don't want vs the low risk strains that just product warts.
http://www.cdc.gov/std/hpv/stdfact-hpv.htm