How to create new columns based on values in two specific columns of a Spark DataFrame?

I have dataframe :

client  type
------  ----
89      id
56      id
34      id
13      id
67      phone
68      phone

I need create two new column based on column "client" and "type". Where "type" == "id", then client number to column "id", where "type" == "phone", then client number to column "phone"

I tried:

Df.withColumn("id", when($"type" === "id", $"client")).withColumn("phone", when($"type" === "phone", $"client"))

and I get this result :

+--------+----+--------+
|  client|type|id|phone|
+--------+----+--------+
|      89|cuid|89| null|
|      56|cuid|56| null|
|      34|cuid|34| null|
|      13|cuid|13| null|
+--------+-------------+

but expected result is :

+--------+----+----------+
|  client|type|  id|phone|
+--------+----+----------+
|      89|cuid|  89| null|
|      56|cuid|  56| null|
|      34|cuid|  34| null|
|      13|cuid|  13| null|
|      67|cuid|null|   67|
|      68|cuid|null|   68|
+--------+---------------+

You can try something like this:

import pyspark.sql.functions as F

x = [(89, "id"), (56, "id"), (34, "id"), (13, "id"), (67, "phone"), (68, "phone")]

df = (
    spark.createDataFrame(x, schema=["client", "type"])
    .withColumn("id", F.when(F.col("type") == F.lit("id"), F.col("client")))
    .withColumn("phone", F.when(F.col("type") == F.lit("phone"), F.col("client")))
    .show()
)

output:

+------+-----+----+-----+
|client| type|  id|phone|
+------+-----+----+-----+
|    89|   id|  89| null|
|    56|   id|  56| null|
|    34|   id|  34| null|
|    13|   id|  13| null|
|    67|phone|null|   67|
|    68|phone|null|   68|
+------+-----+----+-----+