The stamping of Sale and Purchase Agreement can be done immediately because it's for nominal stamp duties only.

The Principal Loan Agreement (ie. Facilities Agreement) would take slightly longer, probably between 1 to 2 weeks from the date your solicitors submit same for adjudication to determine the stamp duty payable. You can get your estimation by doing the following simple equation:-

Loan Amount (minus MRTA, legal fees etc) x 0.5%

I don't think the stamping office will require 3 months to stamp any types of documents. Ask deeper and get the exact reasons why they require 3 months.

Ask the solicitor when was the document submitted for adjudication and then request for a copy of the "Adjudication Notice". They can't lie about that date.