Green’s Dictionary of Slang

furburger n.

[fur n. (1) + play on SE hamburger]

1. [1960s+] the vagina, esp. during the act of cunnilingus when it is ‘eaten’.

2. [1980s] a hairpiece, a wig.

In phrases

eat a furburger (v.)

[1980s+] (US) to perform cunnilingus.