As with Al-Noon Al-Saakinah, Al-meem Al-saakinah has it’s own Tajweed rules.
Rule one: Idghaam Shafawee (Lip-based Merging or Merging with the use of lips).
For any meem saakinah, when a second meem follows it, Idghaam Shafawee is sounded for two counts, i.e. the time it takes to say the words, “one – two”. The condition here is that the latter meem has a fat-ha, dammah or kasra on it. Note a shaddah on the second meem is drawn as a notice of this rule [i.e. it is not there for shaddah purposes].
Examples of Idghaam Shafawee are as follow:
قُلُوبِهِمْ مَرَضٌ لَهُمْ مَا
lahum maa ____quloobihim maradun
__ أَمْ مَنْ فَغَشِيَهُمْ مِنَ _ ____
faghashiyahum mina ______ am man
Simple as that. Practice makes perfect.
–Idghaam [Tajweed Basics: Foundations and More: page 12]
–Sukoon [Gatway To Arabic: page 48]
-Tajweed Rule [Tajweed Basics: Foundations and More: second half page 10]
 -View the document ‘Maakharij Al -Huroof’ or ‘Tajweed Basics: Foundations and More’ pages 3 and 4 titled Origin of Letters