Getting a HPV vaccination is not preventive measure for not spreading the HPV infection to the partner (HPV vaccine does not treat existing HPV infections or genital warts) Also, being treated for genital warts, means getting removal of warts, that reduces, but, not eliminates the HPV infection (you still have some potential to transmit the old infection to your partner).
So, by getting HPV vaccine you gonna protect yourself against some virus types (ones covered with the vaccine), not all.
Also, the vaccine is found to be less effective in people who had already been exposed to one of the HPV types covered by the vaccine.