For Halliday’s own take on this shared approach, see his Introduction to Martin’s Systemic functional grammar: a next step into the theory – axial relations.
Framed as history, from Saussure through Firth, he describes how and why he came up with the approach, and the value of a textbook for doing it...
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[1] A meticulous review of this monograph has begun at Systemic Functional Grammar: A Next Step Into The Theory — Axial Relations.
[2] This is very misleading indeed. Halliday's only comment on Martin's monograph itself was, as stated, that it teaches students 'the principles and practice of using system networks'. The rest of his introduction is an introduction to his theory of SFL. There is no endorsement of a "shared approach" that includes Martin's approach to SFL Theory.