The following tree data structure with methods to serialize and two functions to the tree structure.
The functions do not make much sense, but it is primarily about serialization.

open System.IO
open System.Runtime.Serialization.Formatters.Binary
type BKTree<'a> =
| Node of 'a * Map<int, BKTree<'a>>
| Empty
with
member this.toFile(filename) =
let bf = new BinaryFormatter()
using (File.Open(filename, FileMode.Create))
(fun treeFile -> bf.Serialize(treeFile, this))
static member fromFile(filename) =
let bf = new BinaryFormatter()
using (File.Open(filename, FileMode.Open))
(fun treeFile -> bf.Deserialize(treeFile) :?> BKTree<'a>)

let inline singleton a = Node (a, Map.empty)

let inline node a map = Node (a, map)

let rec insert a key t =
match t with
| Empty -> singleton a
| Node (b, map) ->
match Map.tryFind key map with
| None -> Node (b, Map.add key (singleton a) map)
| Some tree -> Node (b, Map.add key (insert a key tree) map)

let rec fromList a l =
match Seq.isEmpty l with
| true -> Empty
| false->
l
|>Seq.skip 1
|>Seq.groupBy fst
|>Seq.map (fun (k,s)->k,fromList a s)
|>Map.ofSeq
|>node a

> let treeInsert = List.fold (fun acc k-> insert "test" k acc ) Empty [0;2;2;3];;

val treeInsert : BKTree<string> =
Node
("test",
map
[(2, Node ("test",map [(2, Node ("test",map []))]));
(3, Node ("test",map []))])

> let treeFromList = fromList "test" [(0,Empty);(2,Empty);(2,Empty);(3,Empty)];;

val treeFromList : BKTree<string> =
Node
("test",
map
[(2, Node ("test",map [(2, Node ("test",map []))]));
(3, Node ("test",map []))])

As you can see that both trees are identical.
> treeInsert = treeFromList;;
val it : bool = true

The first variant is serialized and deserialized without problems.
> treeInsert.toFile "testOK";;
val it : unit = ()
> let testOK = BKTree<string>.fromFile "testOK";;

val testOK : BKTree<string> =
Node
("test",
map
[(2, Node ("test",map [(2, Node ("test",map []))]));
(3, Node ("test",map []))])

Here occurs when deserializing an error.
> treeFromList.toFile "testFail";;
val it : unit = ()
> let testFail = BKTree<string>.fromFile "testFail";;
System.ArgumentNullException: Value cannot be null.
Parameter name: array
at Microsoft.FSharp.Collections.FSharpMap`2.OnDeserialized(StreamingContext context)
at System.Runtime.Serialization.SerializationEvents.InvokeOnDeserialized(Object obj, StreamingContext context)
at System.Runtime.Serialization.ObjectManager.RaiseOnDeserializedEvent(Object obj)
at System.Runtime.Serialization.ObjectManager.RegisterObject(Object obj, Int64 objectID, SerializationInfo info, Int64 idOfContainingObj, MemberInfo member, Int32[] arrayIndex)
at System.Runtime.Serialization.Formatters.Binary.ObjectReader.RegisterObject(Object obj, ParseRecord pr, ParseRecord objectPr, Boolean bIsString)
at System.Runtime.Serialization.Formatters.Binary.ObjectReader.ParseObjectEnd(ParseRecord pr)
at System.Runtime.Serialization.Formatters.Binary.ObjectReader.Parse(ParseRecord pr)
at System.Runtime.Serialization.Formatters.Binary.__BinaryParser.Run()
at System.Runtime.Serialization.Formatters.Binary.ObjectReader.Deserialize(HeaderHandler handler, __BinaryParser serParser, Boolean fCheck, Boolean isCrossAppDomain, IMethodCallMessage methodCallMessage)
at System.Runtime.Serialization.Formatters.Binary.BinaryFormatter.Deserialize(Stream serializationStream, HeaderHandler handler, Boolean fCheck, Boolean isCrossAppDomain, IMethodCallMessage methodCallMessage)
at FSI_0002.fromFile@14.Invoke(FileStream treeFile)
at Microsoft.FSharp.Core.Operators.Using[T,TResult](T resource, FSharpFunc`2 action)
at <StartupCode$FSI_0027>.$FSI_0027.main@()
> Stopped due to error