(a) Whenever a tax supported library in a county, township, or municipality has been converted to a public library district under this Article, all of the assets (including any building or buildings (i) solely occupied by and publicly designated as the library building or buildings and (ii) solely used for library purposes) and any liabilities of the public tax supported library’s board of library trustees in connection with the operation of its library shall become the assets and liabilities of the public library district. If the library converted to a public library district was eligible to receive its proportionate share of the Personal Property Tax Replacement Fund, that eligibility shall continue to apply to the public library district created by the conversion.
     (b) Nothing in this Section shall preclude a municipality, township, or county, by written agreement, from sharing a library building or buildings with a district library if the establishment of a district library has been approved and the district includes wholly within its territory a municipal, township, or county library.