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#Mathematica, 46 bytes
Reverse@Select[Array[Fibonacci,t=1+#,0],#<t&]&
Try it online!
thanx to @JungHwan Min for -16 bytes
#Mathematica, 6246 bytes
If[#==1,{1,0},Reverse@Select[s=Array[FibonacciReverse@Select[Array[Fibonacci,t=#t=1+#,0],#<=t&]]&#<t&]&
Try it online!Try it online!
#Mathematica, 62 bytes
If[#==1,{1,0},Reverse@Select[s=Array[Fibonacci,t=#,0],#<=t&]]&
#Mathematica, 4562 bytes
If[#==1,{1,0},Reverse@Select[s=Array[Fibonacci,t=#]t=#,#<=t&]&0],#<=t&]]&
#Mathematica, 45 bytes
Reverse@Select[s=Array[Fibonacci,t=#],#<=t&]&