The answer to your question depends on the laws of Ohio and Florida. Under the Ohio statue, which I referenced originally, a sexual offender must register as follows:
Sexual Offenders: Annually for 10 years
Sexual Predators: Every 90 days for life
Habitual offenders: Annually for 20 years.
So depending on his classification the above will tell you how long he must register had he remained in Ohio.
Under the Florida statue (F.S. 775.21) registration remains for life unless he has had his civil rights restored, received a full pardon or had his conviction overturned. I included section (6) for you.
V. What else must predators do? (See F.S. 775.21(6).).
Registration obligations continue for life unless the predator has had his or her civil rights restored, or has received a full pardon or has had a conviction set aside in a post conviction proceeding for an offense that was used in making the offender a sexual predator. After ten years after release from confinement, supervision, or sanctions (whichever is later) with no arrests for felonies or misdemeanors, a predator may petition the criminal division of circuit court to remove his or her predator designation. The court has discretion to grant or deny the petition.
A predator's failure to register, provide required information, or failure to renew a driver's license or Florida identification card is a third degree felony.
The Florida law reference anyone convicted or found to have committed a sexual offense AFTER 10/01/93 must register. Your boyfriend was convicted in 1987 and obviously this is pre 1993. However, as a result of the dangerousness of not continuing to register in Florida he should arrange an appointment with the Florida probation department of his local court. He should bring with him both his Ohio conviction and probation court paperwork. He should request an official opinion from them in writing.
Most importantly his registration requirement will be governed by the three-conviction status in Ohio; Sexual Offender (10 yrs), Sexual Predator (life), or Habitual offender (20 yrs).
This seems a bit confusing, but it is all dependant of his conviction classification in Ohio.
If you need more clarification don't hesitate to contact me.