Minimisatiom using Myhill-Nerode Theorem I have recently studied the Myhill–Nerode theorem and while applying it to minimize these FSMs, I encountered a problem. Is it always the case that the final states should be grouped together because they are indistinguishable? 

In the first FSM below, if I group states (q3,q4) on 0, q3 reaches q4 and q4 reaches q4, but on 1 both behave differently as q4 has no transition on 1. 

Same trouble with the second FSM.

I want to understand how to group together the states while using the theorem.
In the first automaton, you can see that every accepting state has a transition with 0 to an accepting state, while a transition with 1 goes to either a sink or is just non-existing. But this means that reading a 1 from an accepting state leads always to rejecting the input. Thus, all accepting states are equivalent.

In the second automaton, you can see that $q_2$ has a 0-transition to $q_5$, a non-accepting state, while the other two accepting states have 0-transitions to accepting states. Thus, $q_2$ cannot be equivalent to both $q_4$, and $q_3$. Moreover, $q_3$ and $q_4$ cannot be equivalent because reading 00 from both states leads to different behavior (one run is accepting, th other rejecting). Thus, in this case you cannot merge any of the accepting states.