It depends on one's interpretation of the Treaty on the Non-Proliferation of Nuclear Weapons. Ironically, NATO has previously taken the position that such sharing agreements are allowed as long as the nuclear weapons remain under sole control & command of the nuclear-weapons state which provides them, while Belarus is a member of the Non-Aligned Movement, which puts forward an opposing point of view.
Article I & II of the NPT state:
Article I: Each nuclear-weapons state (NWS) undertakes not to transfer, to any recipient, nuclear weapons, or other nuclear explosive devices, and not to assist any non-nuclear weapon state to manufacture or acquire such weapons or devices.
Article II: Each non-NWS party undertakes not to receive, from any source, nuclear weapons, or other nuclear explosive devices; not to manufacture or acquire such weapons or devices; and not to receive any assistance in their manufacture.
The position of the United States along with key NATO allies is that the sharing of nuclear weapons - for example, the US nuclear weapons stationed in Belgium, Italy, Turkey, Germany, and the Netherlands - is permitted under these articles because the weapons remain under the sole control & command of the US, despite being stationed on foreign territory. According to the alliance's policy document on nuclear sharing:
To guarantee the security of its Allies, the United States has deployed a limited number of B-61 nuclear weapons to certain locations in Europe,
which remain under US custody and control in full compliance with the Treaty on the Non-Proliferation of Nuclear Weapons (NPT). The United States follows strict procedures to guarantee the safety and security of the weapons stationed in Europe at all times.
However, since 1998, Belarus has been a member of the Non-Aligned Movement, which has consistently argued that such sharing agreements constitute breaches of the protocol. In 2015, for instance, the group published a recommendation for inclusion in the Review Conference of the Parties, which stated that one of its objectives was:
To underscore the necessity of the full and non-discriminatory implementation of articles I and II of the Treaty by all States parties, in particular nuclear-weapon States, to prevent the proliferation of nuclear weapons and other nuclear explosive devices, including through nuclear weapon-sharing with other States under any kind of security and military arrangements or alliances
I think it's fairly telling that in the US remarks to the Conference on Disarmament on March 3rd, there was no accusation of a potential breach of any international agreements:
Lukashenka’s continued support for Russia’s unprovoked war against Ukraine is deeply concerning as is the removal of Belarus’ constitutional commitment to remain neutral and nuclear weapon-free. It will make Belarus even more subservient to Russia. Any movement of Russian nuclear weapons into Belarus would be dangerously provocative and further destabilize the region. We call on Belarus to reject Russia’s policies of nuclear threat and intimidation.
I don't think there are any other agreements to which Belarus is a signatory which would affect the legality of such a deployment - the country is not a signatory of the Treaty on the Prohibition of Nuclear Weapons, for example, and the Budapest Memorandum doesn't prohibit such a venture.
