** Shares of Australia's Hotel Property Investments rise as much as 3.7% to A$3.63; set for their best trading session since Sept. 9

** The pub operator's board recommends shareholders to reject the takeover offer from a consortium led by real estate investor Charter Hall

** The latest offer values the pub landlord at A$755.8 mln ($502.91 mln)

** Co says offer undervalues the firm and its prospects while raising questions about its timing

** Stock has risen 22% this year, as of last close

($1 = 1.5029 Australian dollars)

(Reporting by Rishav Chatterjee in Bengaluru)

((Rishav.Chatterjee@thomsonreuters.com;))