Hi ,
First pls check your setting for MM period through Tcode OMSY..Refer below screen shot..
You can close the MM period through Tcode - MMPV. Just want to clear that ,User can post GR in Last month if "Allow posting to Previous Period" flag selected..When you close the period ..last month will be always open.Suppose You close the MM period on Jan 26 .You MM period will be open for Jan & Feb Month.User can do the GR for Month of Jan & Feb.
You can check your current period running through Tcode MMRV.For FI & Costing Period refer tcode - OB52 & OKP1.
Regards
Abhishek Tiwari