I never heard of any long gun restrictions as to buying from other states.
Here is Louisiana's law. I am posting LA because I already know that they can not purchase in FL.
Part III. Purchase of Rifles and Shotguns
1801. Declaration of policy It is declared
that it is in the public interest to authorize residents of this state to purchase or otherwise obtain rifles and shotguns or ammunition in states
contiguous to this state in compliance with such
other laws of this state or its political subdivisions as may be applicable and in compliance
with Section 102 of the Gun Control Act of 1968,
Public Law 90-618, 18 U.S.C.§ 921 et seq. and
it is the declared intention of this state that the
sale of shotguns and rifles and the sale of ammunition in this state to residents of adjacent
states is hereby authorized pursuant to regulations issued under the Gun Control Act of 1968.
1802. Definitions As used in this Part:
(1) "A state contiguous to this state" shall
mean any state having a common border with
this state.
(2) All other terms shall be given the meaning
prescribed in 18 U.S.C.§ 921 (the Gun Control
Act of 1968, Public Law 90-618) and the regulations duly promulgated thereunder as presently enacted or promulgated and as hereafter
modified.
1803. Purchase of rifle or shotgun or ammunition It shall be lawful for any person residing in this state, including any corporation or other business entity maintaining a place of business in this state, to purchase or otherwise obtain a rifle or shotgun or ammunition in any state
which is contiguous to this state and to receive
or transport such rifle or shotgun or ammunition
into this state and to permit any person residing
in a contiguous state to purchase shotguns,
rifles or ammunition in this state and to receive
or transport such rifles, shotguns or ammunition
in this state