Our pilot lost the logbook
We now want to sell the aircraft - can FAA reconstruct the logbooks?


As @fooot mentions in the comments you can find most of the details on this question here. There is a brief AOPA article here.


  If costs are involved can we get the pilot to pay for it?


For this you need to consult a lawyer (I would try and get one that specializes in aviation related cases). Depending on how his contract (if he has one) with your company is arranged you may have some weight here. There is a nice document covering a lot of cases in this space that you can find here. See section VI, but you may be covered for this under your insurance, 


  VI. LOST, STOLEN OR DESTROYED LOGBOOKS
  MAY BE COVERD UNDER THE AIRCRAFT'S
  INSURANCE POLICY.
  
  Lost or destroyed logbooks may be covered under the aircraft’s
  insurance policy. However, whether or not coverage exists will depend
  on the language of the policy and, if the logbooks are not
  specifically covered under the policy, an insurer can deny coverage
  and a court may have to decide whether coverage exists.


I would seriously take time to look for them prior to doing anything as Im sure you already have. You can take a look at this thread for some info on rebuilding logs.  

It is also worth reaching out the aviation shop that you use to maintain the plane. Many shops may have work records on file that can help you rebuild your records.