How would I translate "与君知"
My translation would be something like "With your knowledge" with the understanding that "your" refers to somebody of a higher status, usually either due to them being royalty or them being immensely respected and of a good moral character (or both!). 

To explain, 与 means "with" or "and," a meaning that has not changed much since ancient times. You see it a lot in formal writing, and even in some jargon (e.g. 与门 refers to the AND gate of a logical circuit). In this particular context, it is clear that it probably means "with" as it appears to be a preposition more than a conjunction.

In classical Chinese (文言文), one typically finds the usage of 君 to mean roughly the same as 您 i.e. a polite, honorific pronoun to address somebody of a higher status. 

From 有道词典：


  封建时代指帝王、诸侯等，引申为人的尊称，相当于“您”。道德品行良好的人也可称君子。


which, roughly translated, means that during feudal times, 君 referred to kings, princes etc, and others would use it to respectfully address them, equivalent to today's 您. The word 君子 can also be used to refer to somebody with high moral standards and good character. 

知 refers to knowledge. You may be familiar with the term 知道 in modern Chinese which means "to know."