It has been provided in the Act that on conversion of a firm/private company/unlisted public company into LLP, any approval, permit, or license issued to the firm/private company/unlisted company under any other Act shall, subject to the provisions of such other Act under which such approval, permit, or license was issued, be transferred in the name of the converted entity, viz LLP.
Therefore, you may approach the PF and ESIC departments to initiate the change process.