What are considered the summer months abbreviations?
According to the US Government Printing Office's (GPO) Style
Manual the summer months are never abbreviated, but always spelled
to avoid confusion.
So you must spell out June and July according the
August, a summer month, can be abbreviated to Aug.
September, again a summer month, can be abbreviated to
May, though not a summer month, is never abbreviated
since it is only three letter long.
These are the GPO style guide lines.
In day to day practice though June is often abbreviated
to Jun. and July is abbreviated to Jul., but
as you can see a typo if one letter can cause confusion as to which
month is meant.