no it wasn't
Kappa Phi Lambda - fraternity - ended in 1874.
Phi Beta Kappa is in reference to the first letters of each word in the Greek saying philosiphia biou kubernetes which translates to philosophy the guide of life. Phi Beta Kappa is a name used for U.S. fraternity and sorority organizations.
Phi Kappa National Fraternity was created on 1900-02-03.
Kappa Phi Lambda - fraternity - was created on 1862-08-03.
Phi Sigma Beta is a fraternity that was founded at Howard University in Washington, DC. The official animal of the fraternity is the dove.
The motto of Phi Kappa National Fraternity is 'Highest in brotherhood, greatest ever known!'.
Kappa Phi Lambda - fraternity -'s motto is 'Mentes Multæ Consilium Unum'.
Phi Kappa Phi and Phi Beta Kappa are both honor societies, but they have different focuses and membership criteria. Phi Kappa Phi is open to top-performing students across all academic disciplines, while Phi Beta Kappa is specifically for students in the liberal arts and sciences. Phi Beta Kappa is also older and more selective, with a strong emphasis on the liberal arts tradition.
There was never a connection. And there is no such letter from Diggs to Phi beta sigma asking them to join Kappa Alpha Psi. No sigma has seen such a letter nor members of Kappa Alpha Psi. There were two letters written one from Diggs to college men that were not organized explaining the orgins of Kappa, and another from a fraternity to Kappa asking to join, but nothing came of it. Yet, testimony to such a letter has persisted through the years and it appears evident through the annals of history that some form of communication did materialize between the fraternities of Kappa Alpha Psi and the Phi Beta Sigma. According to page 97 of a book entitied Black Greek-letter Organization in the Twenty-first Century the following historical account is noted: "It was at this time that the fraternity [Phi Beta Sigma] had another unique opportunity to expand. In a letter dated December 11, 1915, Kappa Alpha Psi Fraternity founder and Grand Polemarch Elder W. Diggs offered to merge Kappa Alpha Psi with Phi Beta Sigma. At the time, Kappa was establishing itself in the Midwest, while Sigma was expanding in the East and South. The fraternity's general board considered the proposal, but in a reply dated December 18, 1915, [Abram Langston] Taylor turned down the offer."
Phi Beta Delta - fraternity - was created in 1912.
Phi Beta Kappa Society was created on 1776-12-05.
Phi Beta Kappa Memorial Hall was created in 1957.